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arXiv · 1509.01887

New examples of period collapse

Dan Cristofaro-Gardiner·Teresa Xueshan Li·Richard Stanley
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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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Dan Cristofaro-Gardiner, Teresa Xueshan Li, Richard Stanley. 2015-09-07. New examples of period collapse. https://arxiv.org/abs/1509.01887

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