caa a22 4500 445358734 CHVBK 20180317142908.0 cr unu---uuuuu 170323e20110301xx s 000 0 eng 10.1007/s00493-011-2644-1 doi (NATIONALLICENCE)springer-10.1007/s00493-011-2644-1 Björner Anders Institut Mittag-Leffler, Auravägen 17, S-182 60, Djursholm, Sweden aut A q -analogue of the FKG inequality and some applications [Elektronische Daten] [Anders Björner] Let L be a finite distributive lattice and µ: L → ℝ+ a log-supermodular function. For functions k: L → ℝ+ let $E_\mu (k;q)^{\underline{\underline {def}} } \sum\limits_{x \in L} {k(x)\mu (x)q^{rank(x)} \in \mathbb{R}^ + [q]} .$ We prove for any pair g,h: L → ℝ+ of monotonely increasing functions, that $E_\mu (g;q) \cdot E_\mu (h;q) \ll E_\mu (1;q) \cdot E_\mu (gh;q),$ 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. János Bolyai Mathematical Society and Springer Verlag, 2011 Combinatorica Springer-Verlag 31/2(2011-03-01), 151-164 0209-9683 31:2<151 2011 31 493 https://doi.org/10.1007/s00493-011-2644-1 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00493-011-2644-1 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Björner Anders Institut Mittag-Leffler, Auravägen 17, S-182 60, Djursholm, Sweden aut NATIONALLICENCE 773 0- Combinatorica Springer-Verlag 31/2(2011-03-01), 151-164 0209-9683 31:2<151 2011 31 493 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer