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no. 3
On the Todd class of the permutohedral variety
Castillo, Federico1; Liu, Fu2
1 Max Planck Institutefor Mathematics in the Sciences Inselstr. 22 04103 Leipzig Germany
2 Department of Mathematics University of California, Davis One Shields Avenue, Davis, CA 95616 USA.
Algebraic Combinatorics, Volume 4 (2021) no. 3, pp. 387-407.

In the special case of braid fans, we give a combinatorial formula for the Berline–Vergne’s construction for an Euler–Maclaurin type formula that computes the number of lattice points in polytopes. Our formula is obtained by computing a symmetric expression for the Todd class of the permutohedral variety. By showing that this formula does not always have positive values, we prove that the Todd class of the permutohedral variety X d is not effective for d≥24.

Additionally, we prove that the linear coefficient in the Ehrhart polynomial of any lattice generalized permutohedron is positive.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/alco.157
Classification: 52B20, 14M25
Keywords: Ehrhart polynomials, generalized permutohedra, Berline–Vergne construction

Castillo, Federico 1; Liu, Fu 2

1 Max Planck Institutefor Mathematics in the Sciences Inselstr. 22 04103 Leipzig Germany
2 Department of Mathematics University of California, Davis One Shields Avenue, Davis, CA 95616 USA.
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Castillo, Federico; Liu, Fu. On the Todd class of the permutohedral variety. Algebraic Combinatorics, Volume 4 (2021) no. 3, pp. 387-407. doi : 10.5802/alco.157. https://alco.centre-mersenne.org/articles/10.5802/alco.157/

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