BettiBounds

Macaulay2 package BettiBounds: Bounds for the Betti numbers of iterated stellar subdivisions of the boundary of a simplex. Using unprojection theory we give in [6] bounds for the Betti numbers of the Stanley-Reisner ring of a stellar subdivision of a Gorenstein* simplicial complex. Applying this result we obtain a bound for the total Betti numbers of iterated stellar subdivisions of the boundary complex of a simplex. This bound depends only on the number of stellars and we construct examples which prove that it is sharp. The purpose of this package is to give an implementation of this construction. Using Kustin-Miller addition of Betti tables, we provide an efficient way to compute the graded Betti tables of the examples. This works far beyond the range in which the resolution or even ideal can be computed directly. This package requires the package SimplicialComplexes.m2 version 1.2 or higher, so install this first.

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References in zbMATH (referenced in 1 article , 1 standard article )

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  1. Böhm, Janko; Papadakis, Stavros Argyrios: Bounds for the Betti numbers of successive stellar subdivisions of a simplex (2015)