New examples of period collapse

2015/09/07 by Dan Cristofaro-Gardiner, Dan Cristofaro‐Gardiner, Cristofaro-Gardiner, Dan +5
Engineering · Mathematics · #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Symplectic Geometry (math.SG) #graph theory and CDMA systems #math.CO #math.SG

paper · pdf · doi:10.48550/arxiv.1509.01887

20 pages

arxiv created 2015/09/07 · openalex publication_date 2015/09/07 · arxiv updated 2015/09/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

"Period collapse" refers to any situation where the period of the Ehrhart function of a polytope is less than the denominator of that polytope. We study several interesting situations where this occurs, primarily involving triangles. For example: 1) we determine exactly when the Ehrhart function of a right triangle with legs on the axes and slant edge with irrational slope is a polynomial; 2) we find triangles with periods given by any even-index k-Fibonacci number, and larger denominators; 3) we construct several higher dimensional examples. Several related issues are also discussed, including connections with symplectic geometry.

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