Thomas Zaslavsky

Publications and So Forth by Topic

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* Abstracts, announcements, summaries, and essentially expository works.
† Secondary classification.

Index of Topics

• Combinatorics
• Hyperplane and Other Arrangements
  • Hyperplane Arrangements
  • Other Arrangements
• Matroid Theory
• Graph Theory
• Signed Graphs
  • Graph Theory
  • Matroids
  • Coloring and Chromatic Invariants
  • Surface Embedding
  • Other
• Gain and Biased Graphs
  • Graph Theory
  • Matroids
  • Coloring and Invariants
  • Other
• Coding
• Lattice-Point Counting
• Sperner Theory
• Algebra
• Analysis
• Miscellaneous

Combinatorics

Hyperplane and Other Arrangements

• Hyperplane Arrangements

  • Facing up to Arrangements: Face-Count Formulas for Partitions of Space by Hyperplanes. Thesis (MIT, 1974) and Mem. Amer. Math. Soc., No. 154, Amer. Math. Soc., Providence, R.I., 1975.
    • Selections reprinted in J.P.S. Kung, ed., A Source Book in Matroid Theory, Birkhauser, Boston, 1986, pp. 309-331 with editorial commentary pp. 278-282.
  • "Maximal dissections of a simplex". J. Combinatorial Theory Ser. A, 20 (1976), 244-257.
  • * "Arrangements of hyperplanes; matroids and graphs". Proc. Tenth Southeastern Conf. on Combinatorics, Graph Theory and Computing (Boca Raton, 1979), Vol. II, pp. 895-911. Utilitas Math. Publ. Inc., Winnipeg, Man., 1979.
  • "The slimmest arrangements of hyperplanes: II. Basepointed geometric lattices and Euclidean arrangements". Mathematika, 28 (1981), 169-190.
  • † "Bicircular geometry and the lattice of forests of a graph". Quart. J. Math. Oxford (2), 33 (1982), 493-511.
  • "The slimmest arrangements of hyperplanes: I. Geometric lattices and projective arrangements". Geometriae Dedicata, 14 (1983), 243-259.
  • "On the interpretation of Whitney numbers through arrangements of hyperplanes, zonotopes, non-Radon partitions, and orientations of graphs" (with Curtis Greene). Trans. Amer. Math. Soc., 280 (1983), 97-126.
  • "Extremal arrangements of hyperplanes". Discrete Geometry and Convexity (Proc., New York, 1982), Ann. New York Acad. Sci., 440 (1985), 69-87.
  • † "Orientation of signed graphs". Europ. J. Combinatorics, 12 (1991), 361-375.
  • "Perpendicular dissections of space". Discrete Comput. Geom., 27 (2002), 303-351.
  • "Faces of a hyperplane arrangement enumerated by ideal dimension, with application to plane, plaids, and Shi". Geom. Dedicata, 98 (2003), 63-80.
  • † "Biased graphs. IV: Geometrical realizations". J. Combinatorial Theory Ser. B, 89 (2003), no. 2, 231-297.
  • "Inside-out polytopes" (with Matthias Beck). Advances in Math., 205 (2006), no. 1, 134-162.
  • "An enumerative geometry for magic and magilatin labellings" (with Matthias Beck). Ann. Combin., 10 (2006), no. 4, 395-413.
  • "Six little squares and how their numbers grow" (with Matthias Beck). J. Integer Sequences, 13 (2010), Article 10.6.2.
  • "The number of nowhere-zero flows in graphs and signed graphs" (with Matthias Beck). J. Combinatorial Theory Ser. B, 96 (2006), no. 6, 901-918.
  • ""Lattice point counts for the Shi arrangement and other affinographic hyperplane arrangements" (with David Forge). J. Combinatorial Theory Ser. A, 114 (2007), no. 1, 97-109.
  • "Nonattacking queens in a rectangular strip" (with Seth Chaiken and Christopher R.H. Hanusa). Ann. Combinatorics, 14 (2010), no. 4, 419-441.
  • † "An elementary chromatic reduction for gain graphs and special hyperplane arrangements" (with Pascal Berthomé, Raul Cordovil, David Forge, and Véronique Ventos). Electronic J. Combinatorics, 16 (1) (2009), Article R121, 31 pp.
  • "Colorations, orthotopes, and a huge polynomial Tutte invariant of weighted gain graphs" (with David Forge). Submitted.

• Other Arrangements (points, spheres, topological hyperplanes)

  • * "Counting the faces of cut-up spaces". Bull. Amer. Math. Soc., 81 (1975), 916-918.
  • "A combinatorial analysis of topological dissections". Advances in Math., 25 (1977), 267-285.
  • "On the interpretation of Whitney numbers through arrangements of hyperplanes, zonotopes, non-Radon partitions, and orientations of graphs" (with Curtis Greene). Trans. Amer. Math. Soc., 280 (1983), 97-126.
  • "Extremal arrangements of hyperplanes". Discrete Geometry and Convexity (Proc., New York, 1982), Ann. New York Acad. Sci., 440 (1985), 69-87.
  • † "Biased graphs. IV: Geometrical realizations". J. Combinatorial Theory Ser. B, 89 (2003), no. 2, 231-297.
  • "On the division of space by topological hyperplanes". European J. Combinatorics, 30 (2009), no. 8, 1835-1845.

Matroid Theory

• "The slimmest arrangements of hyperplanes: II. Basepointed geometric lattices and Euclidean arrangements". Mathematika, 28 (1981), 169-190.
• "The slimmest arrangements of hyperplanes: I. Geometric lattices and projective arrangements". Geometriae Dedicata, 14 (1983), 243-259.
• † "On the interpretation of Whitney numbers through arrangements of hyperplanes, zonotopes, non-Radon partitions, and orientations of graphs" (with Curtis Greene). Trans. Amer. Math. Soc., 280 (1983), 97-126.
• * "The Möbius function and the characteristic polynomial". Chapter 7 of Combinatorial Geometries, ed. Neil White, pp. 114-138. Encyclopedia of Math. and its Appl., Vol. 29. Cambridge Univ. Press, Cambridge, 1987.
• † "Matroids determine the embeddability of graphs in surfaces". Proc. Amer. Math. Soc., 106 (1989), 1131-1135.
• * "Parametrized Tutte invariants". Summary of "Strong Tutte functions of matroids and graphs".
• "Strong Tutte functions of matroids and graphs". Trans. Amer. Math. Soc., 334 (1992), 317-347.

Graph Theory

• * † "Voltage-graphic geometry and the forest lattice". Report on the XVth Denison-OSU Math Conference (Granville, Ohio, 1980), pp. 85-89. Dept. of Math., Ohio State University, Columbus, Ohio, 1980.
• "Complementary matching vectors and the uniform matching extension property". Europ. J. Combinatorics, 2 (1981), 91-103. Correction, ibid., 2(1981), 305.
• "The number of cladistic characters" (with F. R. McMorris). Math. Biosciences, 54 (1981), 3-10.
• "Bound graphs of a partially ordered set" (with F. R. McMorris). J. Combin. Inform. System Sci., 7 (1982), 134-138.
• "Uniform distribution of a subgraph in a graph". Combinatorial Mathematics (Proc. Colloq. Internat., Marseille-Luminy, 1981), ed. C. Berge et al. Ann. Discrete Math., 17 (1983), 657-664.
• "On the interpretation of Whitney numbers through arrangements of hyperplanes, zonotopes, non-Radon partitions, and orientations of graphs" (with Curtis Greene). Trans. Amer. Math. Soc., 280 (1983), 97-126.
• "Generalized matchings and generalized Hermite polynomials". Finite and Infinite Sets (Proc. Sixth Hungarian Colloq. on Combinatorics, Eger, 1981), ed. A. Hajnal, L. Lovasz, and V. T. Sós, Vol. II, pp. 851-865. Colloq. Math. Soc. Janos Bolyai, 37. Soc. Math. Janos Bolyai, Budapest, and North-Holland, Amsterdam, 1984.
• * † "Line graphs of switching classes". Report of the XVIIIth O.S.U. Denison Maths Conference (Granville, Ohio, 1984), pp. 2-4. Dept. of Math., Ohio State Univ., Columbus, Ohio, 1984.
• "Matroids determine the embeddability of graphs in surfaces". Proc. Amer. Math. Soc., 106 (1989), 1131-1135.
• † "Strong Tutte functions of matroids and graphs". Trans. Amer. Math. Soc., 334 (1992), 317-347.
• † "The covering radius of the cycle code of a graph" (with Patrick Solé). Discrete Appl. Math., 45 (1993), 63-70.
• † "Maximality of the cycle code of a graph" (with Patrick Solé). Discrete Math., 128 (1994), 401-405.
• "The number of nowhere-zero flows in graphs and signed graphs" (with Matthias Beck). J. Combinatorial Theory Ser. B, 96 (2006), no. 6, 901-918.

Signed Graphs

• Graph Theory

  • "Characterizations of signed graphs". J. Graph Theory, 5 (1981), 401-406.
  • * "Line graphs of switching classes". Report of the XVIIIth O.S.U. Denison Maths Conference (Granville, Ohio, 1984), pp. 2-4. Dept. of Math., Ohio State Univ., Columbus, Ohio, 1984.
  • "Balanced decompositions of a signed graph". J. Combinatorial Theory Ser. B, 43 (1987), 1-13.
  • "Orientation of signed graphs". Europ. J. Combinatorics, 12 (1991), 361-375.
  • "A coding approach to signed graphs" (with Patrick Solé). SIAM J. Discrete Math., 7 (1994), 544-553.
  • "Signed analogs of bipartite graphs". Discrete Math., 179 (1998), 205-216.
  • "The number of nowhere-zero flows in graphs and signed graphs" (with Matthias Beck). J. Combinatorial Theory Ser. B, 96 (2006), no. 6, 901-918.
  • "A simple algorithm that proves half-integrality of bidirected network programming" (with Ethan D. Bolker). Networks, 48 (2006), no. 1, 36-38.
  • " Resolution of irreducible integral flows on a signed graph " (with Beifang Chen and Jue Wang).

• Matroids

  • "The geometry of root systems and signed graphs". Amer. Math. Monthly, 88, No. 2 (February, 1981), 88-105.
  • * † "Is there a theory of signed graph embedding?" Report on the XVIth Denison-OSU Math conference (Granville, Ohio, 1981), pp. 79-82. Dept. of Math., Ohio State University, Columbus, Ohio, 1981.
  • "Signed graphs". Discrete Appl. Math., 4 (1982), 47-74. Erratum, ibid., 5 (1983), 248.
  • "The biased graphs whose matroids are binary". J. Combinatorial Theory Ser. B, 42 (1987), 337-347.
  • "Biased graphs whose matroids are special binary matroids". Graphs and Combinatorics, 6 (1990), 77-93.
  • † "Orientation of signed graphs". Europ. J. Combinatorics, 12 (1991), 361-375.
  • "Is there a matroid theory of signed graph embedding?". Ars Combinatoria, 45 (1997), 129-141.
  • "The number of nowhere-zero flows in graphs and signed graphs" (with Matthias Beck). J. Combinatorial Theory Ser. B, 96 (2006), no. 6, 901-918.
  • "Inside-out polytopes" (with Matthias Beck). Advances in Math., 205 (2006), no. 1, 134-162.
  • "Other matroids of graphs (Outline)". Unpublished manuscript, 2008.

• Coloring and Chromatic Invariants

  • "The geometry of root systems and signed graphs". Amer. Math. Monthly, 88, No. 2 (February, 1981), 88-105.
  • "Signed graph coloring". Discrete Math., 39 (1982), 215-228.
  • "Chromatic invariants of signed graphs". Discrete Math., 42 (1982), 287-312.
  • † "On the interpretation of Whitney numbers through arrangements of hyperplanes, zonotopes, non-Radon partitions, and orientations of graphs" (with Curtis Greene). Trans. Amer. Math. Soc., 280 (1983), 97-126.
  • "How colorful the signed graph?". Discrete Math., 52 (1984), 279-284.
  • "The signed chromatic number of the projective plane and Klein bottle and antipodal graph coloring". J. Combinatorial Theory Ser. B, 63 (1995), 136-145.
  • "Inside-out polytopes" (with Matthias Beck). Advances in Math., 205 (2006), no. 1, 134-162.
  • "The number of nowhere-zero flows in graphs and signed graphs" (with Matthias Beck). J. Combinatorial Theory Ser. B, 96 (2006), no. 6, 901-918.

• Surface Embedding

  • "Is there a theory of signed graph embedding?" Report on the XVIth Denison-OSU Math conference (Granville, Ohio, 1981), pp. 79-82. Dept. of Math., Ohio State University, Columbus, Ohio, 1981.
  • * "The demigenus of a signed graph". Report on the XXth Ohio State-Denison Mathematics Conference (Granville, Ohio, 1988). Dept. of Math., Ohio State Univ., Columbus, Ohio, 1988.
  • "Orientation embedding of signed graphs". J. Graph Theory, 16 (1992), 399-422.
  • "The projective-planar signed graphs". Discrete Math., 113 (1993), 223-247.
  • "The signed chromatic number of the projective plane and Klein bottle and antipodal graph coloring". J. Combinatorial Theory Ser. B, 63 (1995), 136-145.
  • "The order upper bound on parity embedding of a graph". J. Combinatorial Theory Ser. B, 68 (1996), 149-160.
  • "Is there a matroid theory of signed graph embedding?". Ars Combinatoria, 45 (1997), 129-141.
  • "The largest parity demigenus of a simple graph". J. Combinatorial Theory Ser. B, 70 (1997), 325-345.
  • "The largest demigenus of a bipartite signed graph". Discrete Math., 232 (2001), 189-193.

• Other

  • "Multipartite togs (analogs of two-graphs) and regular bitogs". Proc. Fifteenth Southeastern Conf. on Combinatorics, Graph Theory and Computing (Baton Rouge, 1984), Vol. III, Congressus Numerantium, 45 (1984), 281-293.
  • "Togs (generalizations of two-graphs)". Optimization, Design of Experiments and Graph Theory (Proc. Symp., Bombay, 1986), ed. M.N. Gopalan and G.A. Patwardhan, pp. 314-334. Indian Inst. of Technology, Bombay, 1988.
  • * "A mathematical bibliography of signed and gain graphs and allied areas". Electronic J. Combinatorics, Dynamic Surveys in Combinatorics (1998), Number DS8.
  • * "Glossary of signed and gain graphs and allied areas". Electronic J. Combinatorics, Dynamic Surveys in Combinatorics (1998), Number DS9.

Gain and Biased Graphs

• Graph Theory

  • "Vertices of localized imbalance in a biased graph". Proc. Amer. Math. Soc., 101 (1987), 199-204.
  • "Biased graphs. I. Bias, balance and gains". J. Combinatorial Theory Ser. B, 47 (1989), 32-52.
  • "Cycle and circle tests of balance in gain graphs: Forbidden minors and their groups" (with Konstantin Rybnikov). J. Graph Theory, 51 (2006), no. 1, 1--21.
  • "Criteria for balance in abelian gain graphs, with an application to piecewise-linear geometry" (with Konstantin Rybnikov). Discrete Comput. Geom., 34 (2005), no. 2, 251-268.
  • "Biased graphs. VII. Contrabalance and antivoltages". J. Combinatorial Theory Ser. B, 97 (2007), no. 6, 1019--1040.
  • "Associativity in multary quasigroups: The way of biased expansions". Aequationes Math., to appear.
  • * "Quasigroup associativity and biased expansion graphs". Electron. Res. Announc. Amer. Math. Soc., 12 (2006), 13-18.
  • "Universal and topological gains for biased graphs".

• Matroids

  • † "Maximal dissections of a simplex". J. Combinatorial Theory Ser. A, 20 (1976), 244-257.
  • * "Voltage-graphic matroids". Matroid Theory and Its Applications (Proc. C.I.M.E., Varenna, Italy, 1980), ed. Adriano Barlotti, pp. 417-423. Liguori Editore, Naples, 1982.
  • "Voltage-graphic geometry and the forest lattice". Report on the XVth Denison-OSU Math Conference (Granville, Ohio, 1980), pp. 85-89. Dept. of Math., Ohio State University, Columbus, Ohio, 1980.
  • "Bicircular geometry and the lattice of forests of a graph". Quart. J. Math. Oxford (2), 33 (1982), 493-511.
  • "The biased graphs whose matroids are binary". J. Combinatorial Theory Ser. B, 42 (1987), 337-347.
  • "Biased graphs whose matroids are special binary matroids". Graphs and Combinatorics, 6 (1990), 77-93.
  • "Biased graphs. II. The three matroids". J. Combinatorial Theory Ser. B, 51 (1991), 46-72.
  • "Frame matroids and biased graphs". Europ. J. Combinatorics, 15 (1994), 303-307.
  • † "Biased graphs. III. Chromatic and dichromatic invariants". J. Combinatorial Theory Ser. B, 64 (1995), 17-88.
  • "Supersolvable frame-matroid and graphic-lift lattices". Europ. J. Combinatorics, 22 (2001), 119-133.
  • "Dowling geometries are line closed". Unpublished note, 2001.
  • "Perpendicular dissections of space". Discrete Comput. Geom., 27 (2002), 303-351.
  • † "Faces of a hyperplane arrangement enumerated by ideal dimension, with application to plane, plaids, and Shi". Geom. Dedicata, 98 (2003), 63-80.
  • "Biased graphs. IV: Geometrical realizations". J. Combinatorial Theory Ser. B, 89 (2003), no. 2, 231-297.
  • "Biased graphs. V. Group and biased expansions".
  • "An elementary chromatic reduction for gain graphs and special hyperplane arrangements" (with Pascal Berthomé, Raul Cordovil, David Forge, and Véronique Ventos). Electronic J. Combinatorics, 16 (1) (2009), Article R121.
  • "Biased graphs. VI. Synthetic geometry" (with Rigoberto Flórez).
  • "Biased graphs. VII. Contrabalance and antivoltages". J. Combinatorial Theory Ser. B, 97 (2007), no. 6, 1019--1040.
  • "Geometric lattices of structured partitions: I. Gain-graphic matroids and group-valued partitions".
  • "Geometric lattices of structured partitions: II. Lattices of group-valued partitions based on graphs and sets".
  • "Geometric lattices of structured partitions: III. Composed and sequenced partitions".

• Invariants

  • † "Maximal dissections of a simplex". J. Combinatorial Theory Ser. A, 20 (1976), 244-257.
  • "Bicircular geometry and the lattice of forests of a graph". Quart. J. Math. Oxford (2), 33 (1982), 493-511.
  • "Biased graphs. III. Chromatic and dichromatic invariants". J. Combinatorial Theory Ser. B, 64 (1995), 17-88.
  • "Tractable partially ordered sets derived from root systems and biased graphs" (with Phil Hanlon). Order, 14 (1997-98), 229-257.
  • † "Supersolvable frame-matroid and graphic-lift lattices". Europ. J. Combinatorics, 22 (2001), 119-133.
  • † "Perpendicular dissections of space". Discrete Comput. Geom., 27 (2002), 303-351.
  • † "Faces of a hyperplane arrangement enumerated by ideal dimension, with application to plane, plaids, and Shi". Geom. Dedicata, 98 (2003), 63-80.
  • ""Lattice point counts for the Shi arrangement and other affinographic hyperplane arrangements" (with David Forge). J. Combinatorial Theory Ser. A, 114 (2007), no. 1, 97-109.
  • "Biased graphs. VII. Contrabalance and antivoltages". J. Combinatorial Theory Ser. B, 97 (2007), no. 6, 1019-1040.
  • "A new distribution problem of balls into urns, Stanley's chromatic symmetric function, and gain graphs". Unpublished manuscript, 2007.
  • "Totally frustrated states in the chromatic theory of gain graphs". European J. Combinatorics, 30 (2009), 133-156.
  • "Nonattacking queens in a rectangular strip" (with Seth Chaiken and Christopher R.H. Hanusa). Ann. Combinatorics, 14 (2010), no. 4, 419-441.
  • "Colorations, orthotopes, and a huge polynomial Tutte invariant of weighted gain graphs" (with David Forge). Submitted.
  • "An elementary chromatic reduction for gain graphs and special hyperplane arrangements" (with Pascal Berthomé, Raul Cordovil, David Forge, and Véronique Ventos). Electronic J. Combinatorics, 16 (1) (2009), Article R121.
  • "Biased graphs. V. Group and biased expansions".
  • "Biased graphs. VIII. A cornucopia of examples".

• Other

  • * "A mathematical bibliography of signed and gain graphs and allied areas". Electronic J. Combinatorics, Dynamic Surveys in Combinatorics (1998), Number DS8.
  • * "Glossary of signed and gain graphs and allied areas". Electronic J. Combinatorics, Dynamic Surveys in Combinatorics (1998), Number DS9.

Coding Theory

• "The covering radius of the cycle code of a graph" (with Patrick Solé). Discrete Appl. Math., 45 (1993), 63-70.
• "Maximality of the cycle code of a graph" (with Patrick Solé). Discrete Math., 128 (1994), 401-405.
• "A coding approach to signed graphs" (with Patrick Solé). SIAM J. Discrete Math., 7 (1994), 544-553.

Lattice-Point Counting

• "Inside-out polytopes" (with Matthias Beck). Advances in Math., 205 (2006), no. 1, 134-162.
• "The number of nowhere-zero flows in graphs and signed graphs" (with Matthias Beck). J. Combinatorial Theory Ser. B, 96 (2006), no. 6, 901-918.
• "An enumerative geometry for magic and magilatin labellings" (with Matthias Beck). Ann. Combin., 10 (2006), no. 4, 395-413.
• "Six little squares and how their numbers grow" (with Matthias Beck). J. Integer Sequences, 13 (2010), Article 10.6.2.
• "Biased graphs. VII. Contrabalance and antivoltages". J. Combinatorial Theory Ser. B, 97 (2007), no. 6, 1019--1040.
• "Nonattacking queens in a rectangular strip" (with Seth Chaiken and Christopher R.H. Hanusa). Ann. Combinatorics, 14 (2010), no. 4, 419-441.

Sperner Theory

• "A shorter, simpler, stronger proof of the Meshalkin-Hochberg-Hirsch bounds on componentwise antichains" (with Matthias Beck). J. Combinatorial Theory Ser. A, 100 (2002), 196-199.
• "A Meshalkin theorem for projective geometries" (with Matthias Beck). J. Combinatorial Theory Ser. A, 102 (2003), 433-441.
• "A unifying generalization of Sperner's theorem" (with Matthias Beck and Xueqin Wang). In: Ervin Györi, Gyula O.H. Katona, and Lászlo Lovász, eds., More Sets, Graphs and Numbers. Bolyai Soc. Math. Stud., Vol. 15, pp. 9-24. Springer, Berlin, and János Bolyai Math. Soc., Budapest, 2006.

Assorted Combinatorics

• "Magic squares and nontransitive dice" (with Matthias Beck and Richard Ehrenborg). Amer. Math. Monthly, 111, No. 7 (Aug.-Sept., 2004), 625-626.
• "A new distribution problem of balls into urns, Stanley's chromatic symmetric function, and gain graphs".
• "Nonattacking queens in a rectangular strip" (with Seth Chaiken and Christopher R.H. Hanusa). Ann. Combinatorics, 14 (2010), no. 4, 419-441.

Algebra

• "Avoiding the identity". Problem 10606. Amer. Math. Monthly, 104 (7) (Aug.-Sept., 1997), 664. Solution by Stephen M. Gagola, ibid., 106 (6) (June-July 1999), 590-591.
• "Associativity in multary quasigroups: The way of biased expansions". Aequationes Math., to appear.
• * "Quasigroup associativity and biased expansion graphs". Electron. Res. Announc. Amer. Math. Soc., 12 (2006), 13-18.

Analysis

• * "A circumambulation of spherical designs (A vector mean value theorem)" (with P. D. Seymour). Report of the Special OSU-Denison Maths Conference held in honor of Professor Hans Zassenhaus (Columbus, Ohio, 1982), pp. 38-40. Dept. of Math., Ohio State University, Columbus, Ohio, 1982.
• "Averaging sets: A generalization of mean values and spherical designs" (with P. D. Seymour). Advances in Math., 52 (1984), 213-240.
• "Asymptotic expansions of ratios of coefficients of orthogonal polynomials with exponential weights" (with Attila Maté and Paul Nevai). Trans. Amer. Math. Soc., 287 (1985), 495-505.
• "Periodicity in quasipolynomial convolution" and correction. Electronic J. Combinatorics, 11 (2) (2004-2005), Article R11 and comment.

Miscellaneous

• "The curious behavior of 1/7", Advanced Problem 6661 (with Jeffrey C. Lagarias). Amer. Math. Monthly, 98 (6) (June-July 1991), 559. Solution by K. Ford, ibid., 100 (2) (Feb. 1993), 191-194.

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Last modified 12 September 2007.