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The *g*-theorem matrices are totally nonnegativePrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 2009 (English)In: Journal of combinatorial theory. Series A (Print), ISSN 0097-3165, E-ISSN 1096-0899, Vol. 116, p. 730-732Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

2009. Vol. 116, p. 730-732
##### Keyword [en]

Simplicial polytope; g-theorem; f-vector; Totally nonnegative matrix
##### National Category

Mathematics
##### Identifiers

URN: urn:nbn:se:kth:diva-10373DOI: 10.1016/j.jcta.2008.07.004ISI: 000264406900015Scopus ID: 2-s2.0-60649097921OAI: oai:DiVA.org:kth-10373DiVA, id: diva2:216356
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt467",{id:"formSmash:j_idt467",widgetVar:"widget_formSmash_j_idt467",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt473",{id:"formSmash:j_idt473",widgetVar:"widget_formSmash_j_idt473",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt479",{id:"formSmash:j_idt479",widgetVar:"widget_formSmash_j_idt479",multiple:true});
##### Note

QC 20100712Available from: 2009-05-08 Created: 2009-05-08 Last updated: 2017-12-13Bibliographically approved
##### In thesis

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.

1. Topological Combinatorics$(function(){PrimeFaces.cw("OverlayPanel","overlay216411",{id:"formSmash:j_idt787:0:j_idt791",widgetVar:"overlay216411",target:"formSmash:j_idt787:0:parentLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

doi
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