Products of arithmetic matroids and quasipolynomial invariants of CW-complexes

Delucchi, Emanuele and Moci, Luca (2018) Products of arithmetic matroids and quasipolynomial invariants of CW-complexes. Journal of Combinatorial Theory, Series A, 157. pp. 28-40. ISSN 00973165

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Abstract

In this note we prove that the product of two arithmetic multiplicity functions on a matroid is again an arithmetic multiplicity function. This allows us to answer a question by Bajo–Burdick–Chmutov, concerning the modified Tutte–Krushkal–Renhardy polynomials defined by these authors. Furthermore, we show that the Tutte quasi-polynomial introduced by Brändén and Moci encompasses invariants defined by Beck–Breuer–Godkin–Martin and Duval–Klivans–Martin and can thus be considered as a dichromate for CW complexes.

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