A good leaf order on simplicial trees

2013/07/08 by Faridi, Sara · 1 citation
#13 #5 #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1307.2190

Abstract

Using the existence of a good leaf in every simplicial tree, we order the facets of a simplicial tree in order to find combinatorial information about the Betti numbers of its facet ideal. Applications include an Eliahou-Kervaire splitting of the ideal, as well as a refinement of a recursive formula of Hà and Van Tuyl for computing the graded Betti numbers of simplicial trees.

Cited by

• The Mendez-Pinto-Villarreal Conjecture for some classes of monomial ideals

Related

• The Betti numbers of Stanley-Reisner ideals of simplicial trees
• Simplicial Trees are Sequentially Cohen-Macaulay
• Powers of facet ideals of simplicial trees
• Resolutions of facet ideals
• Algebraic properties of the path ideal of a tree