Kevin Milans : Teaching : Spring 2025 Math571: Combinatorial Analysis 1

Kevin Milans (milans@math.wvu.edu)
Office: Armstrong Hall 408H
Office Hours: M,Thurs 12:00pm-1:00pm, and by appointment
Class Meetings: MWF 9:30am-10:20am in Brooks Hall 302
Home | Course Syllabus (PDF) | Homework

Course Schedule

No. Date Class Summary Section(s) Comments
1 Jan 13 Introduction; Counting Principles 1.1 -
2 Jan 15 Double counting; binomial theorem; stars and bars 1.1 -
3 Jan 17 Identities; Pascal's triangle 1.2 -
- Jan 20 MLK Day -- no class - -
4 Jan 22 Class Canceled - HW1 is available.
5 Jan 24 Identites II 1.2 -
6 Jan 27 Extended binomial coefficient; Delannoy Numbers 1.2
7 Jan 29 Taxi ball/Delannoy Path bijection 1.2 -
8 Jan 31 Graphs; Multinomial Coefficients; Fermat's Little Theorem 1.3 -
9 Feb 3 Ballot Lists 1.3 -
10 Feb 5 Catalan Numbers 1.3 -
11 Feb 7 Recurrence relations; Fibonacci numbers 2.1 HW1 due. HW2 assigned.
12 Feb 10 Characteristic equation; Fibonacci numbers, Binet's formula 2.2 -
13 Feb 12 Inhomogeneous recurrences; regions in plane 2.2 -
14 Feb 14 Recurrences: characteristic equation method I 2.2 -
15 Feb 17 Recurrences: characteristic equation method II 2.2 -
16 Feb 19 Recurrences: generating function method 2.2 -
17 Feb 21 Catalan numbers via generating functions 2.2 HW2 due. HW3 assigned.
18 Feb 24 Recurrences: Substitution, asymptotic analysis I 2.3 -
19 Feb 26 Recurrences: Substitution, asymptotic analysis II 2.3 -
20 Feb 28 Ordinary generating functions 3.1 -
21 Mar 3 Multiset example; Pascal's formula from generating functions 3.1 -
22 Mar 5 Permutation enumerators 3.1 -
23 Mar 7 Midterm Exam -- --
24 Mar 10 Ordinary Generating Functions; Eulerian numbers 3.1 HW3 due. HW4 assigned.
25 Mar 12 Applications; Snake Oil 3.2 -
26 Mar 14 Exponential Generating Functions II; Stirling Numbers 3.3 -
- - Spring Break: March 17-March 21 - -
27 Mar 24 Inclusion/Exclusion 4.1 -
28 Mar 26 Pigeonhole principle 10.1 -
29 Mar 28 Ramsey's Theorem 10.2 HW4 due. HW5 assigned.
30 Mar 31 Poset definition; comparability (di)graph; cover (di)graph; Hasse diagram 12.1 -
31 Apr 2 Poset background: subposets, isomorphism, chains, antichains 12.1 -
32 Apr 4 Poset definitions/examples: ideals, product posets, boolean lattice 12.1 -
33 Apr 7 Boolean lattice; Sperner's Theorem (12.2.15) 12.1 -
34 Apr 9 Dilworth's Theorem 12.1 -
35 Apr 11 Dilworth's Theorem and Konig--Egervary 12.1 HW5 due.
36 Apr 14 Green--Kleitman Theorem; Gallai--Milgram, Berge Conjecture 12.1 -
37 Apr 16 Graded posets; Symmetric Chain Orders I 12.2 -
-- Apr 18 Fall Break: No class - HW6 assigned.
38 Apr 21 Symmetric Chain Orders II; Product of SCO's is an SCO 12.2 -
39 Apr 23 Bracketing decomposition; Bounded integer partiton order 12.2 -
40 Apr 25 Dedekind's Problem; Hansel's Theorem 12.2 -
41 Apr 28 LYM orders, regular covers, normalized matching property 12.2 -
42 Apr 30 LYM implies Strong Sperner; LYM and Symmetric Chain Decomps. 12.2 -
43 May 2 Extensions and Order Dimension 12.3 HW6 due.
- May 6 Final Exam: 2pm-4pm - -
milans@math.wvu.edu