Triangulations of simplices with vanishing local h-polynomial
Algebraic Combinatorics, Volume 3 (2020) no. 6, pp. 1417-1430.

Motivated by connections to intersection homology of toric morphisms, the motivic monodromy conjecture, and a question of Stanley, we study the structure of geometric triangulations of simplices whose local h-polynomial vanishes. As a first step, we identify a class of refinements that preserve the local h-polynomial. In dimensions 2 and 3, we show that all geometric triangulations with vanishing local h-polynomial are obtained from one or two simple examples by a sequence of such refinements. In higher dimensions, we prove some partial results and give further examples.

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DOI: https://doi.org/10.5802/alco.146
Classification: 05E45
Keywords: local h-polynomials, triangulations of simplices, geometric triangulations
de Moura, André 1; Gunther, Elijah 2; Payne, Sam 3; Schuchardt, Jason 4; Stapledon, Alan 

1. Viela do Mato 4 BL A RC Esq Quinta da Beloura 2710-695 Sintra, Portugal
2. Departement of Mathematics David Rittenhouse Lab 209 South 33rd Street Philadelphia, PA 19104-6395, USA
3. UT Austin Departement of Mathematics 2515 Speedway, PMA 8.100 Austin TX 78722, USA
4. UCLA Departement of Mathematics Math. Sciences Building 6363 520 Portola Plaza Los Angeles, CA 90095, USA
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de Moura, André; Gunther, Elijah; Payne, Sam; Schuchardt, Jason; Stapledon, Alan. Triangulations of simplices with vanishing local $h$-polynomial. Algebraic Combinatorics, Volume 3 (2020) no. 6, pp. 1417-1430. doi : 10.5802/alco.146. https://alco.centre-mersenne.org/articles/10.5802/alco.146/

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