New families of highly neighborly centrally symmetric spheres

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New families of highly neighborly centrally symmetric spheres. / Novik, Isabella; Zheng, Hailun.

In: Transactions of the American Mathematical Society, Vol. 375, No. 6, 2022, p. 4445-4475.

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

Harvard

Novik, I & Zheng, H 2022, 'New families of highly neighborly centrally symmetric spheres', Transactions of the American Mathematical Society, vol. 375, no. 6, pp. 4445-4475. https://doi.org/10.1090/tran/8631

APA

Novik, I., & Zheng, H. (2022). New families of highly neighborly centrally symmetric spheres. Transactions of the American Mathematical Society, 375(6), 4445-4475. https://doi.org/10.1090/tran/8631

Vancouver

Novik I, Zheng H. New families of highly neighborly centrally symmetric spheres. Transactions of the American Mathematical Society. 2022;375(6):4445-4475. https://doi.org/10.1090/tran/8631

Author

Novik, Isabella ; Zheng, Hailun. / New families of highly neighborly centrally symmetric spheres. In: Transactions of the American Mathematical Society. 2022 ; Vol. 375, No. 6. pp. 4445-4475.

Bibtex

@article{3b9be7edb7b34c62b3438a570451df4e,
title = "New families of highly neighborly centrally symmetric spheres",
abstract = "Jockusch [J. Combin. Theory Ser. A 72 (1995), pp. 318-321] constructed an infinite family of centrally symmetric (cs, for short) triangulations of 3-spheres that are cs-2-neighborly. Recently, Novik and Zheng [Adv. Math. 370 (2020), 16 pp.] extended Jockusch's construction: for all d and n > d, they constructed a cs triangulation of a d-sphere with 2n vertices, Δdn, that is cs-⌈d/2⌉-neighborly. Here, several new cs constructions, related to Δdn, are provided. It is shown that for all k > 2 and a sufficiently large n, there is another cs triangulation of a (2k − 1)-sphere with 2n vertices that is cs-k-neighborly, while for k = 2 there are Ω(2n) such pairwise non-isomorphic triangulations. It is also shown that for all k > 2 and a sufficiently large n, there are Ω(2n) pairwise non-isomorphic cs triangulations of a (2k − 1)-sphere with 2n vertices that are cs-(k − 1)-neighborly. The constructions are based on studying facets of Δdn, and, in particular, on some necessary and some sufficient conditions similar in spirit to Gale's evenness condition. Along the way, it is proved that Jockusch's spheres Δ3n are shellable and an affirmative answer to Murai-Nevo's question about 2-stacked shellable balls is given.",
author = "Isabella Novik and Hailun Zheng",
note = "Publisher Copyright: {\textcopyright} 2022 American Mathematical Society",
year = "2022",
doi = "10.1090/tran/8631",
language = "English",
volume = "375",
pages = "4445--4475",
journal = "Transactions of the American Mathematical Society",
issn = "0002-9947",
publisher = "American Mathematical Society",
number = "6",

}

RIS

TY - JOUR

T1 - New families of highly neighborly centrally symmetric spheres

AU - Novik, Isabella

AU - Zheng, Hailun

N1 - Publisher Copyright: © 2022 American Mathematical Society

PY - 2022

Y1 - 2022

N2 - Jockusch [J. Combin. Theory Ser. A 72 (1995), pp. 318-321] constructed an infinite family of centrally symmetric (cs, for short) triangulations of 3-spheres that are cs-2-neighborly. Recently, Novik and Zheng [Adv. Math. 370 (2020), 16 pp.] extended Jockusch's construction: for all d and n > d, they constructed a cs triangulation of a d-sphere with 2n vertices, Δdn, that is cs-⌈d/2⌉-neighborly. Here, several new cs constructions, related to Δdn, are provided. It is shown that for all k > 2 and a sufficiently large n, there is another cs triangulation of a (2k − 1)-sphere with 2n vertices that is cs-k-neighborly, while for k = 2 there are Ω(2n) such pairwise non-isomorphic triangulations. It is also shown that for all k > 2 and a sufficiently large n, there are Ω(2n) pairwise non-isomorphic cs triangulations of a (2k − 1)-sphere with 2n vertices that are cs-(k − 1)-neighborly. The constructions are based on studying facets of Δdn, and, in particular, on some necessary and some sufficient conditions similar in spirit to Gale's evenness condition. Along the way, it is proved that Jockusch's spheres Δ3n are shellable and an affirmative answer to Murai-Nevo's question about 2-stacked shellable balls is given.

AB - Jockusch [J. Combin. Theory Ser. A 72 (1995), pp. 318-321] constructed an infinite family of centrally symmetric (cs, for short) triangulations of 3-spheres that are cs-2-neighborly. Recently, Novik and Zheng [Adv. Math. 370 (2020), 16 pp.] extended Jockusch's construction: for all d and n > d, they constructed a cs triangulation of a d-sphere with 2n vertices, Δdn, that is cs-⌈d/2⌉-neighborly. Here, several new cs constructions, related to Δdn, are provided. It is shown that for all k > 2 and a sufficiently large n, there is another cs triangulation of a (2k − 1)-sphere with 2n vertices that is cs-k-neighborly, while for k = 2 there are Ω(2n) such pairwise non-isomorphic triangulations. It is also shown that for all k > 2 and a sufficiently large n, there are Ω(2n) pairwise non-isomorphic cs triangulations of a (2k − 1)-sphere with 2n vertices that are cs-(k − 1)-neighborly. The constructions are based on studying facets of Δdn, and, in particular, on some necessary and some sufficient conditions similar in spirit to Gale's evenness condition. Along the way, it is proved that Jockusch's spheres Δ3n are shellable and an affirmative answer to Murai-Nevo's question about 2-stacked shellable balls is given.

UR - http://www.scopus.com/inward/record.url?scp=85131250693&partnerID=8YFLogxK

U2 - 10.1090/tran/8631

DO - 10.1090/tran/8631

M3 - Journal article

AN - SCOPUS:85131250693

VL - 375

SP - 4445

EP - 4475

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

SN - 0002-9947

IS - 6

ER -

ID: 310503089