New families of highly neighborly centrally symmetric spheres
Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
Standard
New families of highly neighborly centrally symmetric spheres. / Novik, Isabella; Zheng, Hailun.
I: Transactions of the American Mathematical Society, Bind 375, Nr. 6, 2022, s. 4445-4475.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
Harvard
APA
Vancouver
Author
Bibtex
}
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