The g-theorem matrices are totally nonnegative
2009 (English)In: Journal of combinatorial theory. Series A (Print), ISSN 0097-3165, E-ISSN 1096-0899, Vol. 116, 730-732 p.Article in journal (Refereed) Published
The g-theorem proved by Billera, Lee, and Stanley states that a sequence is the g-vector of a simplicial polytope if and only if it is an M-sequence. For any d-dimensional simplicial polytope the face vector is gM(d) where M-d is a certain matrix whose entries are sums of binomial coefficients. Bjorner found refined lower and upper bound theorems by showing that the (2 x 2)-minors of M-d are nonnegative. He conjectured that all minors of M-d are nonnegative and that is the result of this note.
Place, publisher, year, edition, pages
2009. Vol. 116, 730-732 p.
Simplicial polytope; g-theorem; f-vector; Totally nonnegative matrix
IdentifiersURN: urn:nbn:se:kth:diva-10373DOI: 10.1016/j.jcta.2008.07.004ISI: 000264406900015ScopusID: 2-s2.0-60649097921OAI: oai:DiVA.org:kth-10373DiVA: diva2:216356
QC 201007122009-05-082009-05-082010-12-03Bibliographically approved