Toric arc schemes and $q$-enumeration of lattice points

Autor:	Anderson, Dave, Shah, Aniket
Rok vydání:	2023
Předmět:	Mathematics - Algebraic Geometry Mathematics - Combinatorics
Druh dokumentu:	Working Paper
Popis:	We introduce a natural weighted enumeration of lattice points in a polytope, and give a Brion-type formula for the corresponding generating function. The weighting has combinatorial significance, and its generating function may be viewed as a generalization of the Rogers-Szeg\H{o} polynomials. It also arises from the geometry of the toric arc scheme associated to the normal fan of the polytope. We show that the asymptotic behavior of the coefficients at $q = 1$ is Gaussian. Comment: 22 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2302.03761 Zobrazit plný text záznamu View this record from Arxiv