An upper bound for the multiplicity and Wilf's conjecture for one-dimensional Cohen-Macaulay rings

TL;DR

This paper establishes an upper bound for the multiplicity of certain one-dimensional Cohen-Macaulay rings, characterizes cases of equality, and explores connections with Wilf's conjecture, proving an analogue for almost Gorenstein rings.

Contribution

It introduces a new upper bound for multiplicity in one-dimensional Cohen-Macaulay rings and extends Wilf's conjecture to almost Gorenstein rings.

Findings

Derived an upper bound for multiplicity under specific conditions

Characterized rings that achieve the bound

Proved an analogue of Wilf's conjecture for almost Gorenstein rings

Abstract

In this work we provide an upper bound for the multiplicity of a one-dimensional Cohen-Macaulay ring (under certain conditions), describe the rings attaining the equality for this bound, and outline a connection with Wilf's conjecture for numerical semigroup rings. Then we prove the analogue of Wilf's conjecture for almost Gorenstein rings.