Khovanskii's theorem and effective results on sumset structure

DOI10.19086/da.28814zbMath1484.13040arXiv2009.02140OpenAlexW4225663425MaRDI QIDQ5028491

Michael J. Curran, Leo Goldmakher

Publication date: 10 February 2022

Published in: discrete Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2009.02140

zbMATH Keywords

Ehrhart theoryiterated sumsets

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry) (52B20) Toric varieties, Newton polyhedra, Okounkov bodies (14M25) Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series (13D40) Lattices and convex bodies (number-theoretic aspects) (11H06)

Cites Work

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• Polynomial growth of sumsets in abelian semigroups
• On the structure of the sumsets
• Generalizations of Khovanskiĭ's theorems on the growth of sumsets in abelian semigroups
• Newton polyhedron, Hilbert polynomial, and sums of finite sets
• The Frobenius postage stamp problem, and beyond
• Algebraic Proof for the Geometric Structure of Sumsets
• Points entiers dans les polyèdres convexes
• Short rational generating functions for lattice point problems
• A tight structure theorem for sumsets
• Computing the Continuous Discretely
• Sums of Finite Sets of Integers

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