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math.CO2026
On Unavoidable Faces of High-Dimensional Polytopes
Jesús A. De Loera, Ethan X. Fang, Shengtao Guo +2
Kalai's cube--simplex conjecture asserts that for all positive integers , there is an integer such that every polytope of dimension at least has eit…
math.CO2026
Sharp Bounds on the Independence Number of Simplicial Spheres
Jesús A. De Loera, Ethan X. Fang, Junwei Lu +2
We study the maximum size of an independent set in the graph of a simplicial sphere. Let denote this maximum over all simplicial -spheres on vertices, and let $…