Wilf's conjecture in fixed multiplicity
Combinatorics
2019-07-23 v2 Commutative Algebra
Abstract
We give an algorithm to determine whether Wilf's conjecture holds for all numerical semigroups with a given multiplicity , and use it to prove Wilf's conjecture holds whenever . Our algorithm utilizes techniques from polyhedral geometry, and includes a parallelizable algorithm for enumerating the faces of any polyhedral cone up to orbits of an automorphism group. We also introduce a new method of verifying Wilf's conjecture via a combinatorially-flavored game played on the elements of a certain finite poset.
Cite
@article{arxiv.1903.04342,
title = {Wilf's conjecture in fixed multiplicity},
author = {Winfried Bruns and Pedro Garcia-Sanchez and Christopher O'Neill and Dane Wilburne},
journal= {arXiv preprint arXiv:1903.04342},
year = {2019}
}