BIJECTIVE PROOF PROBLEMS
August 18, 2009
Richard P. Stanley
The statements in each problem are to be proved combinatorially, in most
cases by exhibiting an explicit bijection between two sets. Try to
Universal Cycles
2011
Yu She
Wirral Grammar School for Girls
Department of Mathematical Sciences
University of Liverpool
Supervisor: Professor P. J. Giblin
Contents
1 Introduction
2
2 De
2.1
2.2
2.3
2
TILING PROBLEMS: FROM DOMINOES, CHECKERBOARDS,
AND MAZES TO DISCRETE GEOMETRY
BERKELEY MATH CIRCLE
1. Looking for a number
Consider an 8 8 checkerboard (like the one used to play chess) and consider 3
Lecture Notes
Combinatorics
Lecture by Torsten Ueckerdt
Problem Classes by Jonathan Rollin
Lecture Notes by Stefan Walzer Errors go here. Thanks!
Last updated: July 22, 2015
1
Contents
0 What is Combi
THE q-SERIES IN COMBINATORICS;
PERMUTATION STATISTICS
(Preliminary version)
May 5, 2011
Dominique Foata and Guo-Niu Han
Guo-Niu Han
I.R.M.A. UMR 7501
Universite Louis Pasteur et CNRS
7, rue Rene-Desca
Some simple graph spectra
The (ordinary) spectrum of a graph is the spectrum of its (0,1) adjacency
matrix. (There are other concepts of spectrum, like the Laplace spectrum or
the Seidel spectrum, tha
Topics in generating functions
Qiaochu Yuan
Massachusetts Institute of Technology
Department of Mathematics
Written for the Worldwide Online Olympiad Training program
http:/www.artofproblemsolving.com
Counting spanning trees
Lector: Alexander Mednykh
Sobolev Institute of Mathematics
Novosibirsk State University
Winter School in Harmonic Functions on Graphs
and Combinatorial Designs
20 - 24 January,
Math 296. Homework 1 (Due January 14, 2011)
The Cantor Problem Set: . . . the most astonishing product of mathematical thought, the most beautiful realization
of human activity in the domain of the pu
CSE 713: Random Graphs and Applications
SUNY at Buffalo, Fall 2003
Lecturer: Hung Q. Ngo
Scribe: Hung Q. Ngo
Lecture 10: Introduction to Algebraic Graph Theory
Standard texts on linear algebra and alg
Advanced Graph Algorithms
Jan-Apr 2014
Lecture 24 April 23, 2014
Lecturer: Sanjukta Roy
1
Scribe: Sanjukta Roy
Overview
In the last presentation the lemma of Gessel-Viennot was presented. Today we wil
May 25, 2002 12:26 WSPC/Guidelines
01167
International Journal of Modern Physics B, Vol. 16, Nos. 14 & 15 (2002) 19511961
c World Scientific Publishing Company
DIMERS AND SPANNING TREES: SOME RECENT R
Fractals, Graphs, and Fields
Franklin Mendivil
1. INTRODUCTION. One of the most amazing facets of mathematics is the experience of starting with a problem in one area of mathematics and then following
Lecture 10
Proof of the Matrix-Tree Theorem
The proof here is derived from a terse account in the lecture notes from a course on
Algebraic Combinatorics taught by Lionel Levine at MIT in Spring 2011.1
Enumerative Combinatorics 5:
q-analogues
Peter J. Cameron
Autumn 2013
In a sense, a q-analogue of a combinatorial formula is simply another
formula involving a variable q which has the property that,
Lecture 7
The Matrix-Tree Theorem
This section of the notes introduces a very beautiful theorem that uses linear algebra
to count trees in graphs.
Reading:
The next few lectures are not covered in Jun
PARTITION BIJECTIONS, A SURVEY
IGOR PAK
Abstract. We present an extensive survey of bijective proofs of classical partitions identities. While most bijections are known, they are often presented
in a
The Matrix-Tree Theorem
Evans Doe Ocansey ([email protected])
African Institute for Mathematical Sciences (AIMS)
Supervised by: Prof. Stephan Wagner
Stellenbosch University, South Africa
19 May 2011
Su
TOPICS IN ALGEBRAIC COMBINATORICS
Richard P. Stanley
Version of 1 February 2013
4
CONTENTS
Preface
3
Notation
6
Chapter 1
Walks in graphs
9
Chapter 2
Cubes and the Radon transform
21
Chapter 3
Random
Notes on partitions and their generating functions
1. Partitions of n.
In these notes we are concerned with partitions of a number n, as opposed to partitions of a set.
A partition of n is a combinati
De Bruijn Cycles for Covering Codes
Fan Chung and Joshua N. Cooper
Department of Mathematics
University of California, San Diego, La Jolla, CA
August 4, 2003
Abstract
A de Bruijn covering code is a q-
arXiv:math/9903025v2 [math.CO] 3 Apr 2000
Trees and Matchings
Richard W. Kenyon
James G. Propp
David B. Wilson
Laboratoire de Topologie
University of Wisconsin
Microsoft Research
Universite Paris-Sud
10
Hadamard Matrices
Hadamard Matrix: An n n matrix H with all entries 1 and HH > = nI is called a
Hadamard matrix of order n. For brevity, we use + instead of 1 and
Examples:
[+]
"
+ +
+
2
#
+ + + +
Partitions, permutations and posets
Pter Csikvri
In this note I only collect those things which are not discussed in R. Stanleys
Algebraic Combinatorics book.
1. Partitions
For the denition of (number
"Professor Andrey" Mishchenko Math 296 Lecture Notes
Nick Wasylyshyn
January 24-28, 2010
January 28 : Complex Topology and Analysis
Last class period, there wasnt enough time to discuss everything tha
"Professor" Andrey Mishchenko Math 296 Lecture Notes
Nick Wasylyshyn
January 24-28, 2010
January 25 : Complex Polynomials
Preliminary notes
There will be a quiz tomorrow ! Review notes and definitions
"Professor" Andrey Mishchenko Math 296 Lecture Notes
Nick Wasylyshyn
January 24-28, 2010
January 26 : The Geometry of the Complex Numbers
Before we discuss the geometry of C, we should consider a few
"Professor" Andrey Mishenko Math 296 Lecture Notes
Nick Wasylyshyn
January 24-28, 2010
January 24 : An Introduction to Complex Numbers
Preliminary notes
There will be a quiz sometime this week. As wit