Combinatorics and N-Koszul algebras
Roland Berger
TL;DR
This paper introduces combinatorial methods for analyzing N-Koszul algebras using Hilbert series, with applications such as a new perspective on the MacMahon Master Theorem.
Contribution
It presents novel combinatorial approaches to Hilbert series in N-Koszul algebras and applies them to classical combinatorial identities.
Findings
Introduction of numerical and comodule Hilbert series combinatorics
Applications to the MacMahon Master Theorem
New insights into algebraic combinatorics
Abstract
The numerical Hilbert series combinatorics and the comodule Hilbert series combinatorics are introduced, and some applications are presented, including the MacMahon Master Theorem.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Advanced Combinatorial Mathematics · Polynomial and algebraic computation