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Pattern containment in random permutationsPrimeFaces.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}); (English)Manuscript (preprint) (Other academic)
##### Abstract [en]

##### National Category

Mathematics
##### Identifiers

URN: urn:nbn:se:liu:diva-100894OAI: oai:DiVA.org:liu-100894DiVA: diva2:664202
#####

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Available from: 2013-11-14 Created: 2013-11-14 Last updated: 2013-11-14Bibliographically approved
##### In thesis

This paper studies permutation statistics that count occurrences of patterns. Their expected values on a product of t permutations chosen randomly from Γ S_{n,} where G is a union of conjugacy classes, are considered. Hultman has described a method for computing such an expected value, denoted E_{Γ}(s, t), of a statistic s, when Γ is a union of conjugacy classes of S_{n}. The only prerequisite is that the mean of s over the conjugacy classes is written as a linear combination of irreducible characters of S_{n}. Therefore, the main focus of this article is to express the means of pattern-counting statistics as such linear combinations. A procedure for calculating such expressions for statistics counting occurrences of classical and vincular patterns of length 3 is developed, and is then used to calculate all these expressions. The results can be used to compute E_{Γ}(s, t) for all the above statistics, and for all functions on Sn that are linear combinations of them.

1. The k-assignment polytope, phylogenetic trees, and permutation patterns$(function(){PrimeFaces.cw("OverlayPanel","overlay653747",{id:"formSmash:j_idt712:0:j_idt716",widgetVar:"overlay653747",target:"formSmash:j_idt712:0:parentLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

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