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### The possible sign patterns of the coefficients of Ehrhart polynomials

**Algebra & Discrete Mathematics**

Speaker: | Akiyoshi Tsuchiya, Osaka U |

Related Webpage: | https://www.researchgate.net/profile/Akiyoshi_Tsuchiya |

Location: | 1147 MSB |

Start time: | Mon, Feb 1 2016, 1:10PM |

The Ehrhart polynomial of an integral convex polytopes counts lattice points under dilations of the polytopes. In this talk I will discuss the possible sign patterns of the coefficients of Ehrhart polynomials. While the leading terms, the second leading terms and the constant of Ehrhart polynomials are always positive, the other terms aren't necessarily positive and few examples of Ehrhart polynomials with negative coefficients were known before. I will describe a construction of Ehrhart polynomials with various sign patterns.