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 is not effective for .
Additionally, we prove that the linear coefficient in the Ehrhart polynomial of any lattice generalized permutohedron is positive.
Revised:
Accepted:
Published online:
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 = {http://www.numdam.org/articles/10.5802/alco.157/} }
TY - JOUR AU - Castillo, Federico AU - Liu, Fu TI - On the Todd class of the permutohedral variety JO - Algebraic Combinatorics PY - 2021 SP - 387 EP - 407 VL - 4 IS - 3 PB - MathOA foundation UR - http://www.numdam.org/articles/10.5802/alco.157/ DO - 10.5802/alco.157 LA - en ID - ALCO_2021__4_3_387_0 ER -
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. http://www.numdam.org/articles/10.5802/alco.157/
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