Affiliation:
1. Sant'Agata di Militello
Abstract
Let $K$ be a field and $S=K[x_1,\ldots,x_n]$ a standard polynomial ring over $K$.
In this paper, we give new combinatorial 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 $S$.
Some technical tools allowing to compute the cardinality of $t$-spread strongly stable sets avoiding their construction are also presented.
Such functions are also implemented in a \emph{Macaulay2} package, \texttt{TSpreadIdeals}, to ease the computation of well-known results about algebraic invariants for $t$-spread ideals.
Publisher
The International Electronic Journal of Algebra
Subject
Algebra and Number Theory
Reference17 articles.
1. L. Amata, Graded Algebras: Theoretical and Computational Aspects, Doctoral Thesis, University of Catania, 2020.
2. L. Amata and M. Crupi, Extremal Betti numbers of $t$-spread strongly stable ideals, Mathematics, {7}(8) (2019), 695 (16 pp).
3. L. Amata and M. Crupi, On the extremal Betti numbers of squarefree monomial ideals, Int. Electron. J. Algebra, {30} (2021), 168-202.
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5. L. Amata, M. Crupi and A. Ficarra, Projective dimension and Castelnuovo-Mumford regularity of $t$-spread ideals, Internat. J. Algebra Comput., 32(4) (2022), 837-858.