# Computational methods for t-spread monomial ideals

@inproceedings{Amata2021ComputationalMF, title={Computational methods for t-spread monomial ideals}, author={Luca Amata}, year={2021} }

Let K be a field and S = K[x1, . . . , xn] 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 Macaulay2 package, TSpreadIdeals, providing methods to easily manage t-spread…

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SHOWING 1-10 OF 12 REFERENCES

Extremal Betti Numbers of t-Spread Strongly Stable Ideals

- MathematicsMathematics
- 2019

Let K be a field and let S = K[x1, . . . , xn] be a polynomial ring over K. We analyze the extremal Betti numbers of special squarefree monomial ideals of S known as the t-spread stronglystable…

t-Spread strongly stable monomial ideals*

- MathematicsCommunications in Algebra
- 2019

Abstract We introduce the concept of t-spread monomials and t-spread strongly stable ideals. These concepts are a natural generalization of strongly stable and squarefree strongly stable ideals. For…

ON THE EXTREMAL BETTI NUMBERS OF SQUAREFREE MONOMIAL IDEALS

- MathematicsInternational Electronic Journal of Algebra
- 2021

Let $K$ be a field and $S = K[x_1,\dots,x_n]$ be a polynomial ring over $K$. We discuss the behaviour of the extremal Betti numbers of the class of squarefree strongly stable ideals. More precisely,…

Restricted classes of veronese type ideals and algebras

- Computer Science, MathematicsInt. J. Algebra Comput.
- 2021

This paper focuses on Veronese ideals of bounded support, which are ideals which are generated by monomials of degree $d$ in the polynomial ring in variables and which satisfy certain numerical side conditions regarding their exponents.

Kruskal-Katona Theorem for t-spread strongly stable ideals.

- Mathematics
- 2018

We prove that any t-spread strongly stable ideal has a unique t-spread lex ideal with the same f-vector. We also characterize the possible f-vectors of t-spread strongly stable ideals in the…

Combinatorial Commutative Algebra

- Mathematics
- 2004

Monomial Ideals.- Squarefree monomial ideals.- Borel-fixed monomial ideals.- Three-dimensional staircases.- Cellular resolutions.- Alexander duality.- Generic monomial ideals.- Toric Algebra.-…

Extremal Betti Numbers and Applications to Monomial Ideals

- Mathematics
- 1998

Recall that the (Mumford-Castelnuovo) regularity of M is the least integer ρ such that for each i all free generators of Fi lie in degree ≤ i + ρ, that is βi,j = 0, for j > i + ρ. In terms of…

Extremal Betti numbers of graded modules

- Mathematics
- 2016

Let $S$ be a polynomial ring in $n$ variables over a field $K$ of characteristic $0$. A numerical characterization of all possible extremal Betti numbers of any graded submodule of a finitely…

Monomial Ideals

- 2001

Monomial ideals form an important link between commutative algebra and combinatorics. In this chapter, we demonstrate how to implement algorithms in Macaulay 2 for studying and using monomial ideals.…

Powers of t-spread principal Borel ideals

- MathematicsArchiv der Mathematik
- 2019

We prove that t-spread principal Borel ideals are sequentially Cohen–Macaulay and study their powers. We show that these ideals possess the strong persistence property and compute their limit depth.