The stresses on centrally symmetric complexes and the lower bound theorems

Research output: Contribution to journal › Journal article › Research › peer-review

Standard

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

Harvard

Novik, I & Zheng, H 2021, 'The stresses on centrally symmetric complexes and the lower bound theorems', Algebraic Combinatorics, vol. 4, no. 3, pp. 541-549. https://doi.org/10.5802/ALCO.168

APA

Novik, I., & Zheng, H. (2021). The stresses on centrally symmetric complexes and the lower bound theorems. Algebraic Combinatorics, 4(3), 541-549. https://doi.org/10.5802/ALCO.168

Vancouver

Novik I, Zheng H. The stresses on centrally symmetric complexes and the lower bound theorems. Algebraic Combinatorics. 2021;4(3):541-549. https://doi.org/10.5802/ALCO.168

Author

Novik, Isabella ; Zheng, Hailun. / The stresses on centrally symmetric complexes and the lower bound theorems. In: Algebraic Combinatorics. 2021 ; Vol. 4, No. 3. pp. 541-549.

Bibtex

@article{f5e0cf3ebf6740be84df51aaad6f1c4c,
title = "The stresses on centrally symmetric complexes and the lower bound theorems",
abstract = "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.",
keywords = "Centrally symmetric, Cohen–Macaulay complexes, Face numbers, Polytopes, Stress spaces",
author = "Isabella Novik and Hailun Zheng",
note = "Publisher Copyright: {\textcopyright} The journal and the authors, 2021.",
year = "2021",
doi = "10.5802/ALCO.168",
language = "English",
volume = "4",
pages = "541--549",
journal = "Algebraic Combinatorics",
issn = "2589-5486",
publisher = "Centre Mersenne",
number = "3",

}

RIS

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