Theses and Dissertations

Date of Award

8-1-2024

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematics

First Advisor

Alexey Garber

Second Advisor

Alexey Glazyrin

Third Advisor

Brandt Kronholm

Abstract

Ehrhart theory is a classical topic for polygons or polytopes with vertices with integer coordinates. One of the main results of the theory claims that for every convex polygon P with integer vertices, the number of integer points in its nth dilation is a polynomial in n, the Ehrhart polynomial of P. This property can be extended if for a polynomial weight w(x, y), we sum values of w(x, y) over all points with integer coordinates in the nth dilation of P. The resulted polynomial is called the weighted Ehrhart polynomial of P associated with the weight w. In this thesis we show that weighted Ehrhart polynomials could be used to recognize triangles with integer coordinates. Particularly, we show that if two primitive triangles share weighted Ehrhart polynomials for all weights of degree at most 2, then the triangles coincide.

Comments

Copyright 2024 Rafael Sarabia. https://proquest.com/docview/3116142323

Download

Included in

Mathematics Commons

Share

COinS