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Numrering	Referens	Omslagsbild	Hitta
1.	Doolittle, Joseph, et al. (författare) Partition and Cohen-Macaulay extenders 2022 Ingår i: European journal of combinatorics (Print). - : Elsevier BV. - 0195-6698 .- 1095-9971. ; 102 Tidskriftsartikel (refereegranskat)abstract If a pure simplicial complex is partitionable, then its h-vector has a combinatorial interpretation in terms of any partitioning of the complex. Given a non-partitionable complex increment , we construct a complex Gamma superset of increment of the same dimension such that both Gamma and the relative complex (Gamma , increment ) are partitionable. This allows us to rewrite the h-vector of any pure simplicial complex as the difference of two h-vectors of partitionable complexes, giving an analogous interpretation of the h-vector of a non-partitionable complex. By contrast, for a given complex increment it is not always possible to find a complex Gamma such that both Gamma and (Gamma , increment ) are Cohen- Macaulay. We characterize when this is possible, and we show that the construction of such a Gamma in this case is remarkably straightforward. We end with a note on a similar notion for shellability and a connection to Simon's conjecture on extendable shellability for uniform matroids.

Doolittle, Joseph, et al. (författare)
Partition and Cohen-Macaulay extenders
2022
Ingår i: European journal of combinatorics (Print). - : Elsevier BV. - 0195-6698 .- 1095-9971. ; 102
Tidskriftsartikel (refereegranskat)abstract
- If a pure simplicial complex is partitionable, then its h-vector has a combinatorial interpretation in terms of any partitioning of the complex. Given a non-partitionable complex increment , we construct a complex Gamma superset of increment of the same dimension such that both Gamma and the relative complex (Gamma , increment ) are partitionable. This allows us to rewrite the h-vector of any pure simplicial complex as the difference of two h-vectors of partitionable complexes, giving an analogous interpretation of the h-vector of a non-partitionable complex. By contrast, for a given complex increment it is not always possible to find a complex Gamma such that both Gamma and (Gamma , increment ) are Cohen- Macaulay. We characterize when this is possible, and we show that the construction of such a Gamma in this case is remarkably straightforward. We end with a note on a similar notion for shellability and a connection to Simon's conjecture on extendable shellability for uniform matroids.

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