A second look at the toric h-polynomial of a cubical complex

Details A second look at the toric h-polynomial of a cubical complex A second look at the toric h-polynomial of a cubical complex

2010-02-18

arxiv.org/abs/1002.3601v3

Mathematics

Combinatorics

Minor corrections

Scientific paper

We provide an explicit formula for the toric $h$-contribution of each cubical shelling component, and a new combinatorial model to prove Clara Chan's result on the non-negativity of these contributions. Our model allows for a variant of the Gessel-Shapiro result on the $g$-polynomial of the cubical lattice, this variant may be shown by simple inclusion-exclusion. We establish an isomorphism between our model and Chan's model and provide a reinterpretation in terms of noncrossing partitions. By discovering another variant of the Gessel-Shapiro result in the work of Denise and Simion, we find evidence that the toric $h$-polynomials of cubes are related to the Morgan-Voyce polynomials via Viennot's combinatorial theory of orthogonal polynomials.

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