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A {$q$}-analogue of the {FKG} inequality and some applications
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0002-7497-2764
2011 (English)In: Combinatorica, ISSN 0209-9683, E-ISSN 1439-6912, Vol. 31, no 2, 151-164 p.Article in journal (Refereed) Published
Abstract [en]

Let L be a finite distributive lattice and mu: L -> R(+) a log-supermodular function k: L -> R(+) let [GRAPHICS] We prove for any pair g, h: L -> R(+) of monotonely increasing functions, that E mu(g; q) . E mu(h; q) << E mu(1; q) . E mu(gh; q), where "<<" denotes coefficientwise inequality of real polynomials. The FKG inequality of Fortuin, Kasteleyn and Ginibre (1971) is the real number inequality obtained by specializing to q=1. The polynomial FKG inequality has applications to f-vectors of joins and intersections of simplicial complexes, to Betti numbers of intersections of Schubert varieties, and to correlation-type inequalities for a class of power series weighted by Young tableaux. This class contains series involving Plancherel measure for the symmetric groups and its poissonization.

Place, publisher, year, edition, pages
2011. Vol. 31, no 2, 151-164 p.
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URN: urn:nbn:se:kth:diva-82460DOI: 10.1007/s00493-011-2644-1ISI: 000293788700002ScopusID: 2-s2.0-80051510904OAI: diva2:498257
QC 20120220Available from: 2012-02-11 Created: 2012-02-11 Last updated: 2012-04-14Bibliographically approved

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Björner, Anders
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