Computational methods for tspread monomial ideals
Abstract
Let $K$ be a field and $S=K[x_1,\ldots,x_n]$ a standard polynomial ring over $K$. In this paper, some new optimized algorithms to compute the smallest $t$spread lexicographic set and the smallest $t$spread strongly stable set containing a given set of $t$spread monomials of $S$ are presented. Some technical tools allowing to compute the cardinality of $t$spread strongly stable sets avoiding their construction are given. Then, a \emph{Macaulay2} package, \texttt{TSpreadIdeals}, providing methods to easily manage $t$spread monomials and $t$spread ideals is implemented. Some functions to ease the calculation of well known results about algebraic invariants for $t$spread ideals are also provided.
 Publication:

arXiv eprints
 Pub Date:
 October 2021
 arXiv:
 arXiv:2110.11801
 Bibcode:
 2021arXiv211011801A
 Keywords:

 Mathematics  Commutative Algebra;
 Mathematics  Combinatorics;
 05E40;
 1304;
 13B25;
 13D02;
 16W50;
 68W30