CiteExport$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_upper_j_idt169",{id:"formSmash:upper:j_idt169",widgetVar:"widget_formSmash_upper_j_idt169",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:upper:exportLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_upper_j_idt175_j_idt177",{id:"formSmash:upper:j_idt175:j_idt177",widgetVar:"widget_formSmash_upper_j_idt175_j_idt177",target:"formSmash:upper:j_idt175:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});

Face numbers of Scarf complexesPrimeFaces.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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2000 (English)In: Discrete & Computational Geometry, ISSN 0179-5376, E-ISSN 1432-0444, Vol. 24, no 3-Feb, p. 185-196Article in journal (Refereed) Published
##### Abstract [en]

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

2000. Vol. 24, no 3-Feb, p. 185-196
##### Keywords [en]

resolutions, polytopes, sets
##### Identifiers

URN: urn:nbn:se:kth:diva-19849ISI: 000087814300005OAI: oai:DiVA.org:kth-19849DiVA, id: diva2:338541
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt721",{id:"formSmash:j_idt721",widgetVar:"widget_formSmash_j_idt721",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt727",{id:"formSmash:j_idt727",widgetVar:"widget_formSmash_j_idt727",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt748",{id:"formSmash:j_idt748",widgetVar:"widget_formSmash_j_idt748",multiple:true});
##### Note

QC 20100525Available from: 2010-08-10 Created: 2010-08-10 Last updated: 2017-12-12Bibliographically approved

Let A be a (d + 1) x d real matrix whose row vectors positively span R-d and which is generic in the sense of Barany and Scarf [BS1]. Such a matrix determines a certain infinite d-dimensional simplicial complex Sigma, as described by Barany et al. [BHS]. The group Z(d) acts on Sigma with finitely many orbits. Let f(i) be the number of orbits of (i + 1)-simplices of Sigma. The sequence f = (f(0), f(1),..., f(d-1)) is the f-vector of a certain triangulated (d - 1)-ball T embedded in Sigma. When A has integer entries it is also, as shown by the work of Peeva and Sturmfels [PS], the sequence of Betti numbers of the minimal free resolution of k[x(1),...,x(d+1)]/I, where I is the lattice ideal determined by A. In this paper we study relations among the numbers f(i). It is shown that f(0), f(1),..., f([(d-3)/2]) determine the other numbers via linear relations, and that there are additional nonlinear relations. In more precise (and more technical) terms, our analysis shows that f is linearly determined by a certain M-sequence (g(0), g(1),..., g([(d-1)/2])). namely, the g-vector of the (d - 2)-sphere bounding T. Although T is in general not a cone over its boundary, it turns out that its f-vector behaves as if it were.

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CiteExport$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_lower_j_idt1897",{id:"formSmash:lower:j_idt1897",widgetVar:"widget_formSmash_lower_j_idt1897",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:lower:exportLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_lower_j_idt1898_j_idt1900",{id:"formSmash:lower:j_idt1898:j_idt1900",widgetVar:"widget_formSmash_lower_j_idt1898_j_idt1900",target:"formSmash:lower:j_idt1898:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});