On the Todd class of the permutohedral variety
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 d24.

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

Received:
Revised:
Accepted:
Published online:
DOI: https://doi.org/10.5802/alco.157
Classification: 52B20,  14M25
Keywords: Ehrhart polynomials, generalized permutohedra, Berline–Vergne construction
@article{ALCO_2021__4_3_387_0,
     author = {Castillo, Federico and Liu, Fu},
     title = {On the {Todd} class of the permutohedral variety},
     journal = {Algebraic Combinatorics},
     pages = {387--407},
     publisher = {MathOA foundation},
     volume = {4},
     number = {3},
     year = {2021},
     doi = {10.5802/alco.157},
     language = {en},
     url = {https://alco.centre-mersenne.org/articles/10.5802/alco.157/}
}
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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