In 1987, Stanley conjectured that if a centrally symmetric Cohen–Macaulay simplicial complex of dimension satisfies for some , then for all . Much more recently, Klee, Nevo, Novik, and Zheng conjectured that if a centrally symmetric simplicial polytope of dimension satisfies for some , then for all . This note uses stress spaces to prove both of these conjectures.
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Accepted:
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Keywords: Cohen–Macaulay complexes, polytopes, centrally symmetric, face numbers, stress spaces.
@article{ALCO_2021__4_3_541_0, author = {Novik, Isabella and Zheng, Hailun}, title = {The stresses on centrally symmetric complexes and the lower bound theorems}, journal = {Algebraic Combinatorics}, pages = {541--549}, publisher = {MathOA foundation}, volume = {4}, number = {3}, year = {2021}, doi = {10.5802/alco.168}, language = {en}, url = {http://www.numdam.org/articles/10.5802/alco.168/} }
TY - JOUR AU - Novik, Isabella AU - Zheng, Hailun TI - The stresses on centrally symmetric complexes and the lower bound theorems JO - Algebraic Combinatorics PY - 2021 SP - 541 EP - 549 VL - 4 IS - 3 PB - MathOA foundation UR - http://www.numdam.org/articles/10.5802/alco.168/ DO - 10.5802/alco.168 LA - en ID - ALCO_2021__4_3_541_0 ER -
%0 Journal Article %A Novik, Isabella %A Zheng, Hailun %T The stresses on centrally symmetric complexes and the lower bound theorems %J Algebraic Combinatorics %D 2021 %P 541-549 %V 4 %N 3 %I MathOA foundation %U http://www.numdam.org/articles/10.5802/alco.168/ %R 10.5802/alco.168 %G en %F ALCO_2021__4_3_541_0
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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