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
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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.
Original language | English |
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Journal | Algebraic Combinatorics |
Volume | 4 |
Issue number | 3 |
Pages (from-to) | 541-549 |
ISSN | 2589-5486 |
DOIs | |
Publication status | Published - 2021 |
Bibliographical note
Publisher Copyright:
© The journal and the authors, 2021.
- Centrally symmetric, Cohen–Macaulay complexes, Face numbers, Polytopes, Stress spaces
Research areas
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