Published March 16, 2018
| Published
Journal Article
Open
Periods of Ehrhart Coefficients of Rational Polytopes
- Creators
- McAllister, Tyrrell B.
- Rochais, Hélène O.
Abstract
Let P⊂R^n be a polytope whose vertices have rational coordinates. By a seminal result of E. Ehrhart, the number of integer lattice points in the kth dilate of P (k a positive integer) is a quasi-polynomial function of k — that is, a "polynomial" in which the coefficients are themselves periodic functions of k. It is an open problem to determine which quasi-polynomials are the Ehrhart quasi-polynomials of rational polytopes. As partial progress on this problem, we construct families of polytopes in which the periods of the coefficient functions take on various prescribed values.
Additional Information
© 2018 Electronic Journal of Combinatorics. Submitted: Apr 7, 2016; Accepted: Mar 5, 2018; Published: Mar 16, 2018. The second author was supported by a Wyoming EPSCoR Research Fellowship.Attached Files
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Additional details
- Eprint ID
- 86713
- Resolver ID
- CaltechAUTHORS:20180530-112034063
- University of Wyoming
- Created
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2018-05-30Created from EPrint's datestamp field
- Updated
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2019-10-03Created from EPrint's last_modified field