Combinatorics II

Combinatorics I

Our Teaching Page has important information for my students. (It has the Notes, Exams and Links from all of my previous courses.)
The Teaching Page has my schedule, LOR guidelines, and Usually Useful Pamphlets. One of them is the Checklist (pdf) which gives pointers on competant mathematical writing. Further information is at our class-archive URL (I email this private URL directly to students).

The various Combinatorial czars who help out.

• Voila! a proof of the Eisenstein Irreducibility Criterion (pdf).
• An intro to the Chromatic polynomial of a graph (pdf); a graphical example of deletion-contraction.
• The Comb quizzes so far (pdf). It also has quzzes from the 2^nd semester.
• Students were shocked! by the Graphic Language of Class-C.
• A std proof of the Inclusion-Exclusion principle (pdf). Some Putnam competition Problems using inclusion-exclusion, e.g B3.2009 (soln).
• Following the well-received Home-B, [due BoC, Monday, 16Oct2017] was a Stirling Example of an in-class exam; the much beloved Class-B.
• Neil Sloane's On-line Encyclopedia of Integer Sequences (OEIS).
• Home-A was due BoC, Wedn., 27Sep2017. The eagerly anticipated Class-A [on Friday, 29Sep2017] was greeted with exclamations of Joy and cries of Dude, it's like --totally-- Binomialistic!
• Our Comb 2017t syllabus [updated 23Sep2017, due to hurricane Irma, and some LaTeX typesetting problems] has exam/microquiz info.
• What fun! Computer-generated pictures of Lmino Tilings (txt), illustrating a geometric induction-argument.
• Please learn the Math-Greek alphabet (pdf), which we will use in class frequently.
• Please verify that you can easily do all the problems on High-school & Calc 1 knowledge review exam.

Our textbook is A Walk Through Combinatorics (4^th edition).

Author:	Miklos Bona	Year:	2017
ISBN:	978-9813148840	Publisher:	World Scientific Publishing

An older edition is   QA164 .B66 2002   at Marston.

Spr2018: MAD4204 4563 Intro.Combinatorics.2 MWF4 LIT201 (SE)

Combinatorics II

End-of-semester Comb-II Individual project

...is be due, slid u n d e r my office door (Little Hall 402, Northeast corner) , by 2PM, Thursday, 26Apr2018.

Project-G must be carefully typed, but diagrams may be hand-drawn.

At all times have a paper copy you can hand-in; I do NOT accept electronic versions. Print out a copy each day, so that you always have the latest version to hand-in; this, in case your printer or computer fails. (You are too old for My dog ate my homework.)

Please follow the guidelines on the Checklist  (pdf, 3pages) to earn full credit.

• Breaking news on the Hadwiger-Nelson problem.
• Available is a light Introduction to Ramsey Theory (pdf). Now has boundedness proof for hypergraph Ramsey numbers.
• An illustration in the gap in Kempe's argument for the 4-color theorem..
• The short Class-G (Wednesday, 11Apr2018) was our last in-class exam for the semester. The essay problem can be stated as the Polygamy problem.
• A proof of the Stable-Marriage lemma. Also, triangles in a lotsa-edges graph.
• Our Home-F appeared on 14Mar2018, and was due BoC on Monday, 19Mar2018 with all team-members present.
  Two examples of the Marriage Lemma are the Distinct-cards & Hunter/Farmer problems. Also, available were several doubly-stochastic matrices showing the upper-bound on the epsilon derived in Hunter/Farmer.
  The in-class portion, Class-F, was Wednesday, 21Mar2018.
• Two example spantree-counting using a reduced-Laplacian matrix (pdf) together with a statement and proof of the Block Upper-Triangular--matrix Lemma.
• In one convenient location:  All 6 Comb II quizzes so far (pdf), as well as all Comb I quizzes. [Wednesday, 14Mar2018]
• Rough, un-proofread notes showing Example uses of Generating-Functions.
• The delightful Home-E was due Mon., 05Feb2018.
  Cute! was the consensus on Class-E, which appeared on Wed., 07Feb2018.
• Generating functions and Herb Wilf's wonderful Generating Functionology, which he has made freely available.
  Also, Philippe Flajolet has made his book Analytic Combinatorics freely available.
• Graph theory.

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