Department of Mathematical Sciences
Binghamton University

Math 386: Combinatorics Homework Assignments

Fall 2009



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HOMEWORK I (8/31)

Due on Tues., 9/1:
Read Ch. 1 intro, Sect. 1.1, beginning of Sect. 1.2.
Do (for class discussion) Ch. 1, ## 1, 2, 3, 5, 10.

Due on Wed., 9/2:
Read Sect. 1.2.
Do (for discussion) Ch. 1, ## 2(again), 12, 14, 16, 17.

Due on Fri., 9/4:
Read Sect. 1.4, 1.6.
Do (for discussion) Ch. 1, ## 15, 22, 24, 38, and A1, A2.

Hand in Tues., 9/8:
Ch. 1, ## 4(a), 7, 21.


Problem Set A


HOMEWORK II (8/31)

Due on Tues. 9/8:
Read Sect. 2.1-2.
Do (for discussion) Ch. 2, ## 2, 4(a).

Due on Wed. 9/9:
Do (for discussion) Ch. 2, ## 1, 3, 4(b), 6, 7.

Due on Fri. 9/11:
Do (for discussion) Ch. 2, # 8.

Hand in Fri., 9/11:
Ch. 1, ## 8, 9.
Ch. 2, ## 4(c), 5(a), 9.

Extra! Extra! Much more about magic squares in only 5 pages.


HOMEWORK III (9/13)

Read Sects. 2.3-5.

Do for discussion on
Tues. 9/15: Ch. 2, ## 8, 9, 11, 13.
Wed. 9/16: Ch. 2, ## 16, 17, 19(a), 22.

Hand in Fri. 9/18: Ch. 2, ## 5(b), 15, 19(b), 28.
(Due before 2:00 p.m. in my mailbox at the Math Dep't or at my office. I gladly accept early homework. No late homeworks.)


HOMEWORK IV (9/18)

Read for Mon.-Tues., 9/21-22: Sects. 2.6, 4.2.
Read for Wed., 9/21-22: Sect. 5.1.

Do for discussion on
Tues., 9/22: Ch. 2, ## 31, 34, 41, 60; Ch. 4, # 6(a), 7(a).
Wed., 9/23: Ch. 2, ## 39, 48, 63; Ch. 4, ## 5, 8(b); Ch. 5, # 2.
Fri., 9/25: Ch. 2, # 50; Ch. 5, ## 1, 3.

Hand in Thursday, 9/24 by 4:00 p.m.: Ch. 2, ## 40, 51, 64(a); Ch. 4, ## 6(b), 7(b), 8(c), 9.


TEST I is on Tuesday, Sept. 29!


HOMEWORK V (9/29)

Read for Fri., 10/2: Sects. 5.1-2.

Do for discussion on
Fri., 10/2: Ch. 5, ## 2, 3, 4-6, 7-8, 15, and especially B2.
Mon., 10/5: Ch. 5, ## 9, 16, 23, and especially B3.
Tues., 10/6: Ch. 5, ## 18, 24, B1. (Keep a copy of your proof when you submit this.)

Hand in Wed., 10/7: # B1 and ## 10, 13, 25.


Problem Set B


HOMEWORK VI (10/6)

Read for Wed., 10/7: Sects. 5.3-4.
Read for Fri., 10/9: Sects. 5.4-5 and Meshalkin's Theorem.

Do for discussion on
Fri., 10/9: Ch. 5, ## 14, 19, 22, and C1(a-h), C2. (In #14, don't assume k ≤ r.)
Mon., 10/12: Ch. 5, ## 17, 18, 20, and C1(i), C4. In #20, simplify your answer as far as you can.
Tues., 10/13: Ch. 5, ## 29, 30, 35, 37, 39, and C3.

Hand in Wed., 10/14: Ch. 5, ## 11, 21, 31, 44, and C1(j), C5.
(Warning: This is a long one; prepare days ahead.)

Grading of # 31: 4+4: 4 for how convincing your proof is, 4 for how good your method or technique is.
Grading of # C1(j): 4+4+(bonus 2): 4 for the values, 4 for an explicit general formula, 2 (bonus) for a proof.
Grading of # C5: 4+4: 4 for formula and proof, 4 for series expansion.

Problem Set C


HOMEWORK VII (10/15)

Read for Fri., 10/16: Sect. 6.1.

Read for Mon., 10/17: Sects. 6.2-3.

Do for discussion on
Mon., 10/19: Ch. 6, ## 1, 3, 17.
Tues., 10/20: # D1; also Ch. 6, ## 4, 7, 11.
Wed., 10/21: Ch. 6, ## 10, 12.
Fri., 10/23: Ch. 6, ## 6, 15, 20, 21.

Hand in Fri., 10/23: # D2; also Ch. 6, ## 5, 8, 14, 16.


Problem Set D

Here are two simple problems in extremal set theory (which means problems like Sperner's Theorem, but they don't necessarily use Sperner's Theorem).

TEST II is on Tuesday, Oct. 27. It will cover Homework Sets V-VII. The grades should be in on Friday, Oct. 30.


HOMEWORK VIII (10/24)

Read for Fri., 10/30: Sect. 6.4.

Read for Mon., 11/2: Sect. 6.5.

Do for discussion on
Mon., 11/2: Ch. 6, ## 24(a), 25, 30, and ## E1, E2
Tues., 11/3: Ch. 6, ## 24(b), 27, 33, and ## E3, E4.

Hand in Wed., 11/4: Ch. 6, ## 21, 24(c), 28, 29.


Problem Set E


HOMEWORK SET IX (10/24)

Read for Fri. 11/6: Section 3.1.

Do for discussion on
Mon. 11/9: Ch. 3, ## 1, 4, 5, 7.
Tues. 11/10: Ch. 3, ## 2, 3, 9, 16 (see
remark).
Wed. 11/11: Ch. 3, ## 18, 26.

Hand in Fri. 11/13:
Ch. 3, ## 1 (for k = 23), 6, 11, 15, and # F1, F2.


Problem Set F


HOMEWORK SET X (11/13)

Read for Mon., 11/16: Section 3.2.

Do for discussion on:
Tues. 11/17: Ch. 3, ## 8, 13, 14, 28, and # G2.

Hand in Fri. 11/20: Ch. 3, ## 1 (for k = 23, 24), 17, 19, and # G1.


Problem Set G


HOMEWORK SET XI (11/17-19)

Read for Fri., 11/20: Sections 7.1-2.

Read for Mon., 11/23: Section 7.4 to the middle of p. 236.

Do for discussion on:
Tues. 11/24: Ch. 7, ## 1(a), 2, 4, 8, 13(a-c), 14(a-c), 17, 34.

Hand in by Wed. 11/25 before noon at my office or mailbox:
Ch. 7, ## 13(d), 14(d,e), 33 (using g.f.).


HOMEWORK SET XII (11/19-24,12/1)

Read for Mon., 11/30: Sections 7.4-6.

Do for discussion on:
Wed. 12/2: Ch. 7, ## 37, 46 (by g.f.), 48(e), 50, 52, 53.

Hand in either: Thurs. 12/3 (at my office or mailbox by 4:00), if you want them back on Friday, or: Fri. 12/4:

Ch. 7, ## 14(d)(find a formula for hn), 41 (& find initial condition; note that the diagonals here cannot meet at their endpoints), 48(c), 51.


TEST III is on Tuesday, Dec. 8. It will cover Homework Sets VIII-XII. The grades should be in on Friday, Dec. 11.


HOMEWORK SET XIII (12/1,6)

Read for Wed., 12/9:
Section 10.1: pp. 341-344 (omit the GCD algorithm pp. 344-346), Thm. 10.1.2 (omit proof), Cor. 10.1.3.
Section 10.4: pp. 368-374, Thm. 10.4.4 (omit example), pp. 376-377.

Do for discussion on:
Wed. 12/9: Ch. 10, ## 1, 3, 8, 13, 38, 42, 48.

Do for discussion on:
Fri. 12/11: Ch. 7, # 7 (optional challenge problem).

Hand in Fri. 12/11:
Ch. 10, # 41.



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