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Title:  A statistic on involutions 
Authors:  DEODHAR, RS SRINIVASAN, MK 
Keywords:  finite vectorspaces formula 
Issue Date:  2001 
Publisher:  KLUWER ACADEMIC PUBL 
Citation:  JOURNAL OF ALGEBRAIC COMBINATORICS, 13(2), 187198 
Abstract:  We define a statistic, called weight, on involutions and consider two applications in which this statistic arises. Let I(n) denote the set of all involutions on [n](={1,2,..., n}) and let F(2n) denote the set of all fixed point free involutions on [2n]. For an involution delta, let \ delta \ denote the number of 2cycles in delta. Let [n](q)=1+q+...+q(n1) and let ((n)(k))(q) denote the qbinomial coefficient. There is a statistic wt on I(n) such that the following results are true. (i) We have the expansion [GRAPHICS] (ii) An analog of the (strong) Bruhat order on permutations is defined on F(2n) and it is shown that this gives a rank2((n)(2)) graded ELshellable poset whose order complex triangulates a ball. The rank of delta is an element ofF(2n) is given by wt(delta) and the rank generating function is [1](q)[3](q)...[2n1](q). 
URI:  http://dx.doi.org/10.1023/A:1011249732234 http://dspace.library.iitb.ac.in/xmlui/handle/10054/9719 http://hdl.handle.net/10054/9719 
ISSN:  09259899 
Appears in Collections:  Article

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