Computational methods for t-spread monomial ideals

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International Electronic Journal of Algebra
Volume:35 Issue:35
Computational methods for t-spread monomial ideals

Computational methods for t-spread monomial ideals

Pages : 186-216

View : 69 | Download : 43

Publication Date : 2024-01-09

Article Type : Research Paper

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.
Keywords : Squarefree monomial ideal, t spread ideal, strongly stable ideal, lexicographic ideal, extremal Betti number, computational algebra

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