The stresses on centrally symmetric complexes and the lower bound theorems
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The stresses on centrally symmetric complexes and the lower bound theorems. / Novik, Isabella; Zheng, Hailun.
In: Algebraic Combinatorics, Vol. 4, No. 3, 2021, p. 541-549.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - The stresses on centrally symmetric complexes and the lower bound theorems
AU - Novik, Isabella
AU - Zheng, Hailun
N1 - Publisher Copyright: © The journal and the authors, 2021.
PY - 2021
Y1 - 2021
N2 - In 1987, Stanley conjectured that if a centrally symmetric Cohen–Macaulay simplicial complex ∆ of dimension d − 1 satisfies hi(∆) = (di ) for some i > 1, then hj(∆) = (dj ) for all j > i. Much more recently, Klee, Nevo, Novik, and Zheng conjectured that if a centrally symmetric simplicial polytope P of dimension d satisfies gi(∂P) = (di ) − ( i−d1 ) for some d/2 > i > 1, then gj(∂P) = (dj ) − ( j−d1 ) for all d/2 > j > i. This note uses stress spaces to prove both of these conjectures.
AB - In 1987, Stanley conjectured that if a centrally symmetric Cohen–Macaulay simplicial complex ∆ of dimension d − 1 satisfies hi(∆) = (di ) for some i > 1, then hj(∆) = (dj ) for all j > i. Much more recently, Klee, Nevo, Novik, and Zheng conjectured that if a centrally symmetric simplicial polytope P of dimension d satisfies gi(∂P) = (di ) − ( i−d1 ) for some d/2 > i > 1, then gj(∂P) = (dj ) − ( j−d1 ) for all d/2 > j > i. This note uses stress spaces to prove both of these conjectures.
KW - Centrally symmetric
KW - Cohen–Macaulay complexes
KW - Face numbers
KW - Polytopes
KW - Stress spaces
UR - http://www.scopus.com/inward/record.url?scp=85109317744&partnerID=8YFLogxK
U2 - 10.5802/ALCO.168
DO - 10.5802/ALCO.168
M3 - Journal article
AN - SCOPUS:85109317744
VL - 4
SP - 541
EP - 549
JO - Algebraic Combinatorics
JF - Algebraic Combinatorics
SN - 2589-5486
IS - 3
ER -
ID: 276387541