The stresses on centrally symmetric complexes and the lower bound theorems
Algebraic Combinatorics, Volume 4 (2021) no. 3, pp. 541-549.

In 1987, Stanley conjectured that if a centrally symmetric Cohen–Macaulay simplicial complex Δ of dimension d-1 satisfies h i (Δ)=d i for some i1, then h j (Δ)=d j for all ji. Much more recently, Klee, Nevo, Novik, and Zheng conjectured that if a centrally symmetric simplicial polytope P of dimension d satisfies g i (P)=d i-d i-1 for some d/2i1, then g j (P)=d j-d j-1 for all d/2ji. This note uses stress spaces to prove both of these conjectures.

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DOI: 10.5802/alco.168
Classification: 05E45, 05E40, 13F55, 52B05, 52B15
Keywords: Cohen–Macaulay complexes, polytopes, centrally symmetric, face numbers, stress spaces.
Novik, Isabella 1; Zheng, Hailun 2

1 Department of Mathematics University of Washington Seattle, WA 98195-4350, USA
2 Department of Mathematical Sciences University of Copenhagen Universitesparken 5, 2100 Copenhagen, Denmark
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Novik, Isabella; Zheng, Hailun. The stresses on centrally symmetric complexes and the lower bound theorems. Algebraic Combinatorics, Volume 4 (2021) no. 3, pp. 541-549. doi : 10.5802/alco.168. http://www.numdam.org/articles/10.5802/alco.168/

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