Multibasic Ehrhart theory
Aki Mori, Takeshi Morita, Akihiro Shikama
TL;DR
This paper extends Ehrhart theory to a multibasic setting, introducing new polynomials and series, and establishing an analogue of Ehrhart reciprocity within this framework.
Contribution
It presents the first multibasic extension of Ehrhart polynomials and series, along with a reciprocity theorem analogous to the classical case.
Findings
Defined multibasic Ehrhart polynomials and series
Proved Ehrhart reciprocity analogue for multibasic case
Established foundational properties of the multibasic Ehrhart theory
Abstract
In the present paper, we introduce a multibasic extension of the Ehrhart theory. We give a multibasic extension of Ehrhart polynomials and Ehrhart series. We also show that an analogue of Ehrhart reciprocity holds for multibasic Ehrhart polynomials.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Molecular spectroscopy and chirality · Algebraic structures and combinatorial models