Wilf's conjecture in fixed multiplicity

2019/03/11 by Bruns, Winfried, Garcia-Sanchez, Pedro, O'Neill, Christopher +1
#Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1903.04342

Abstract

We give an algorithm to determine whether Wilf's conjecture holds for all numerical semigroups with a given multiplicity m, and use it to prove Wilf's conjecture holds whenever m ≤ 18. 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.

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