arXiv Open Access 2022

Refined Ehrhart series and bigraded rings

Praise Adeyemo Balazs Szendroi

Lihat Sumber

Abstrak

We study a natural set of refinements of the Ehrhart series of a closed polytope, first considered by Chapoton. We compute the refined series in full generality for a simplex of dimension d, a cross-polytope of dimension d, respectively a hypercube of dimension d<4, using commutative algebra. We deduce summation formulae for products of q-integers with different arguments, generalizing a classical identity due to MacMahon and Carlitz. We also present a characterisation of a certain refined Eulerian polynomial in algebraic terms.

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Penulis (2)

Praise Adeyemo

Balazs Szendroi

Format Sitasi

APA MLA BibTeX

Adeyemo, P., Szendroi, B. (2022). Refined Ehrhart series and bigraded rings. https://arxiv.org/abs/2206.15029

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Informasi Jurnal

Tahun Terbit: 2022
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓