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Séminaire Lotharingien de Combinatoire, 84B.88 (2020), 12 pp.

# Federico Castillo and Fu Liu

# On the Todd Class of the Permutohedral Variety

**Abstract.**
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 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: November 20, 2019.
Accepted: February 20, 2020.
Final version: April 30, 2020.

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