@article{Ibarguen2024, 
author = {Jovanny Ibarguen and Daniel S. Moran and Carlos E. Valencia and Rafael H. Villarreal},
title = {The signature of a monomial ideal},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {10},
pages = {27955-27978},
keywords = {irreducible decomposition, monomial ideal, signature, incidence matrix, regular sequences, minimal free resolution},
url = {https://www.sciopen.com/article/10.3934/math.20241357},
doi = {10.3934/math.20241357},
abstract = {The irreducible decomposition of a monomial ideal has played an important role in combinatorial commutative algebra, with applications beyond pure mathematics, such as biology. Given a monomial ideal  I of a polynomial ring  S=k[x] over a field  k and variables  x={x1,…,xn}, its incidence matrix, is the matrix whose rows are indexed by the variables  x and whose columns are indexed by its minimal generators. The main contribution of this paper is the introduction of a novel invariant of a monomial ideal  I, termed its signature, which could be thought of as a type of canonical form of its incidence matrix, and the proof that two monomial ideals with the same signature have essentially the same irreducible decomposition.}
}