Computational methods for t-spread monomial ideals

Yıl 2024, Cilt: 35 Sayı: 35, 186 - 216, 09.01.2024

Luca Amata

https://doi.org/10.24330/ieja.1402973

Öz

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.

Anahtar Kelimeler

Squarefree monomial ideal, $t$-spread ideal, strongly stable ideal, lexicographic ideal, extremal Betti number, computational algebra

Kaynakça

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