Wednesday, July 2 2014
10:00 - 11:00

Alladi Ramakrishnan Hall

Ehrhart Polynomials

Kamalakshya Mahatab


For a polytope P and any positive integer k, let iP(k) denote the number of integral points in the dilation kP of P by a factor k. Ehrhart proved that if vertices of P have integral coordinates, then the function iP is a polynomial in k. This polynomial is called the Ehrhart polynomial of P. If P has vertices with rational coordinates then iP is `almost' a polynomial. The aim of this talk is to give an exposition to Ehrhart polynomials through examples. We will also discuss some basic properties of iP, such as Periodicity and Reciprocity. The theory of Ehrhart polynomials is a very helpful tool in many combinatorial problems; we will see some applications in this talk. This talk requires no prerequisites from the theory of polytopes.

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