A class of square-free monomial ideals associated to two integer sequences

TL;DR

This paper introduces a new class of square-free monomial ideals linked to two integer sequences and provides recursive methods and explicit formulas for their algebraic invariants.

Contribution

It defines a novel class of monomial ideals associated with sequences and derives recursive and explicit formulas for their algebraic invariants.

Findings

Recursive computation of algebraic invariants for the ideals.

Explicit formulas for invariants in special cases.

New connections between integer sequences and monomial ideals.

Abstract

Given two finite sequences of positive integers $\alpha$ and $\beta$, we associate a square free monomial ideal $I_{\alpha,\beta}$ in a ring of polynomials $S$, and we recursively compute the algebraic invariants of $S/I_{\alpha,\beta}$. Also, we give precise formulas in special cases.