Department of Mathematics

West Chester University

**Mathematics Information**

Office: Room 101

25 University Avenue

West Chester, PA 19383

Phone (610) 436-2440

Fax (610) 738-0578

Email: Department Chair

Each Thursday there will be a mathematics seminar (usually in UNA 120 from 3:15-4:15), while colloquium talks will normally be on a Wednesday (usually in UNA 158 from 3:15-4:15).

These seminars/colloquium talks may be by visiting speakers, WCU faculty, or WCU students, and are open to all interested students and faculty.

Send an e-mail to jmclaughl@wcupa.edu, if you would like to be on the e-mail list to receive advance notice of upcoming talks.

Previous Semesters:Spring 2012, Fall 2011, Spring 2011, Fall 2010, Spring 2010, Fall 2009, Spring 2009, Fall 2008, Spring 2008, Fall 2007, Spring 2007, Fall 2006, Summer 2006, Spring 2006,

11:00AM to 12:00PM Conference Room, 25 University Avenue

**Combinatorial Games Theory** **Seminar - I**

11:00AM to 12:00PM Conference Room, 25 University Avenue

**Combinatorial Games Theory** **Seminar - II**

11:00AM to 12:00PM Conference Room, 25 University Avenue

**Combinatorial Games Theory** **Seminar - III**

3:15 to 4:15PM UNA 158

Arithmetic Combinatorics is a rapidly developing area with close connections to number theory, combinatorics, harmonic analysis and ergodic theory. Roughly speaking, the field is concerned with finding and counting arithmetic structures in sets, often contained in the integers, and it includes such seminal results as Szemeredi's Theorem on arithmetic progressions and the Green-Tao Theorem on arithmetic progressions in the primes. Here we give a brief introduction and survey of some foundational results in this area, and later we focus on improvements and generalizations of two theorems of Sarkozy, the qualitative versions of which state that any set of natural numbers of positive upper density necessarily contains two distinct elements which differ by a perfect square, as well as two elements that differ by one less than a prime number. Included will be joint work with Neil Lyall and Mariah Hamel.

**For further information e-mail** mfisher@wcupa.edu or sgupta@wcupa.edu.

11:00AM to 12:00PM Conference Room, 25 University Avenue

**Combinatorial Games Theory** **Seminar - IV**

3:15 to 4:15PM UNA 119

**"PARTITION BIJECTIONS, A SURVEY - II"**

Over the coming weeks we will work through (as much as possible) Pak’s wonderful survey on integer partition bijections. The aim will be to get a better feel for the method of bijective proofs of partition identities and the interplay between combinatorial identities and analytic basic hypergeometric identities.

11:00AM to 12:00PM Conference Room, 25 University Avenue

**Combinatorial Games Theory** **Seminar - V**

3:15 to 4:15PM UNA 119

**"PARTITION BIJECTIONS, A SURVEY - III"**

11:00AM to 12:00PM Conference Room, 25 University Avenue

**Combinatorial Games Theory** **Seminar - VI**

3:15 to 4:15PM UNA 119

**"PARTITION BIJECTIONS, A SURVEY - IV"**

11:00AM to 12:00PM Conference Room, 25 University Avenue

**Combinatorial Games Theory** **Seminar - VII**

11:00AM to 12:00PM Conference Room, 25 University Avenue

**Combinatorial Games Theory** **Seminar - VIII**

3:15 to 4:15PM UNA 119

**"PARTITION BIJECTIONS, A SURVEY - V"**

3:20 to 4:15PM UNA 158

Professor Viorel Nitica(West Chester University Mathematics Department)

Abstract: In this talk we investigate several tiling problems for regions in a square lattice by ribbon L- shaped tetrominoes. One of our results shows that tiling of the first quadrant by ribbon L-tetrominoes is possible only if it reduces to a tiling of the first quadrant by 2x4 and 4x2 rectangles. A consequence of the result is the classification of all rectangles that can be tiled by ribbon L-shaped tetrominoes.

11:00AM to 12:00PM Conference Room, 25 University Avenue

**Combinatorial Games Theory** **Seminar - IX**

3:20 to 4:15PM UNA 158

Arranging 00011101 on a circle, the consecutive triples are exactly the 8 distinct binary triples. Can we do something similar with a larger alphabet and longer strings? These are called DeBruijn cycles and have a long and interesting history. More recently higher dimensional versions called perfect maps have been investigated. Try, for example creating a 9 by 9 array with entries 0,1,2 such that when wrapped on a torus each of the 81 distinct 2 by 2 patterns with 3 symbols appears exactly once. Mathematical and algorithmic questions and applications related to both of these will be presented.

**For further information e-mail** mfisher@wcupa.edu or sgupta@wcupa.edu

3:20 to 4:15PM UNA 158

"A Modification of Sylvester's Four Point Problem"

In 1865, Sylvester posed the problem of finding the probability that four points randomly chosen with a uniform distribution over a compact convex region K in the plane form the vertices of a convex quadrilateral. This led to substantial research on the ratio

rho_K = E(area(T))/area(K) ,

where T denotes a triangle formed by three independent and uniformly distributed points in K. In this talk we consider the problem of studying the behavior of the ratio

rho_P* = E(area(T))/E(L^2) ,

where L is the distance between two independent points with distribution P and T is a triangle with three independent vertices with distribution P. We call this the Modified Sylvester Four Point Problem.

All are welcome to join us for tea in the Students Lounge after the talk.

3:00 to 3:50 PM UNA 158

One of the underlying goals in knot theory is to determine when two knots are equivalent. A knot is simply an embedded circle in space. Therefore, we can try to answer this question with hands-on examples. However, this simple task can become difficult and the need for mathematics becomes relevant. In this talk, we will discuss some basic knot invariants, such as crossing number, and the three Reidemeister move, and then extending them to links.

All are welcome to join us for tea in the Students Lounge after the talk.

Note: Talks will be added to the schedule throughout the semester. Check back for updates.