TY - JOUR
T1 - The Ehrhart and face polynomials of the graph polytope of a cycle
AU - Ehrenborg, Richard
N1 - Publisher Copyright:
© 2023 Elsevier Ltd
PY - 2024/5
Y1 - 2024/5
N2 - We are interested in the polytope consisting of all points in the first orthant such that the sum of two cyclically adjacent coordinates is less than or equal to 1. This polytope is also known as the graph polytope of a cycle. Using spectral techniques, we obtain a determinant for the Ehrhart quasi-polynomial of this polytope and hence also an expression for the volume of this polytope. The spectral techniques also yield a combinatorial expression for the face polynomial of this polytope in terms of matchings of a cycle.
AB - We are interested in the polytope consisting of all points in the first orthant such that the sum of two cyclically adjacent coordinates is less than or equal to 1. This polytope is also known as the graph polytope of a cycle. Using spectral techniques, we obtain a determinant for the Ehrhart quasi-polynomial of this polytope and hence also an expression for the volume of this polytope. The spectral techniques also yield a combinatorial expression for the face polynomial of this polytope in terms of matchings of a cycle.
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U2 - 10.1016/j.ejc.2023.103906
DO - 10.1016/j.ejc.2023.103906
M3 - Article
AN - SCOPUS:85179075889
SN - 0195-6698
VL - 118
JO - European Journal of Combinatorics
JF - European Journal of Combinatorics
M1 - 103906
ER -