@article{10902/27752,
year = {2022},
url = {https://hdl.handle.net/10902/27752},
abstract = {Let π:Rn→Rd  be any linear projection, let A be the image of the standard basis. Motivated by Postnikov’s study of postitive Grassmannians via plabic graphs and Galashin’s connection of plabic graphs to slices of zonotopal tilings of 3-dimensional cyclic zonotopes, we study the poset of subdivisions induced by the restriction of π  to the k-th hypersimplex, for k=1,…,n−1 . We show that: For arbitrary A and for k≤d+1 , the corresponding fiber polytope F(k)(A)  is normally isomorphic to the Minkowski sum of the secondary polytopes of all subsets of A of size max{d+2,n−k+1} . When A=Pn  is the vertex set of an n-gon, we answer the Baues question in the positive: the inclusion of the poset of π -coherent subdivisions into the poset of all π -induced subdivisions is a homotopy equivalence. When A=C(d,n)  is the vertex set of a cyclic d-polytope with d odd and any n≥d+3, there are non-lifting (and even more so, non-separated) π
-induced subdivisions for k=2.},
organization = {The authors were supported by the Einstein Foundation Berlin under grant EVF-2015-230. Work of F. Santos is also supported by grants MTM2017-83750-P/AEI/10.13039/501100011033 and PID2019-106188GB-I00/AEI/10.13039/501100011033 of the Spanish State Research Agency.},
publisher = {Springer},
publisher = {Selecta Mathematica, New Series, 2022, 28, 4},
title = {Hypersimplicial subdivisions},
author = {Olarte, Jorge Alberto and Santos, Francisco},
}