Geodesic
A statistic on involutions
Journal of Algebraic Combinatorics, Tome 13 (2001) no. 2, pp. 187-198.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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](=${1,2,\dots , n}$) and let $F(2 n)$ denote the set of all fixed point free involutions on [$2 n$]. For an involution $( _{k} ^{n} ) q \left( {_{{k}}^{{n}} } \right)$q denote the $q$-binomial coefficient. There is a statistic wt on $I( n)$ such that the following results are true. (i) We have the expansion
Keywords: permutation statistics, $q$-binomial coefficient, Bruhat order, involutions, fixed point free involutions 
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     title = {A statistic on involutions},
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Deodhar, Rajendra S.; Srinivasan, Murali K. A statistic on involutions. Journal of Algebraic Combinatorics, Tome 13 (2001) no. 2, pp. 187-198. http://geodesic.mathdoc.fr/item/JAC_2001__13_2_a2/