115 research outputs found
Specializations and Extensions of the quantum MacMahon Master Theorem
We study some specializations and extensions of the quantum version of the
MacMahon Master Theorem derived by Garoufalidis, Le and Zeilberger. In
particular, we obtain a (t,q)-analogue for the Cartier-Foata noncommutative
version and a semi-strong (t,q)-analogue for the contextual algebra.Comment: 12 page
Fix-Mahonian Calculus, I: two transformations
We construct two bijections of the symmetric group S_n onto itself that
enable us to show that three new three-variable statistics are equidistributed
with classical statistics involving the number of fixed points. The first one
is equidistributed with the triplet (fix,des,maj), the last two with
(fix,exc,maj), where "fix," "des," "exc" and "maj" denote the number of fixed
points, the number of descents, the number of excedances and the major index,
respectively
Fix-Mahonian Calculus, II: further statistics
Using classical transformations on the symmetric group and two
transformations constructed in Fix-Mahonian Calculus I, we show that several
multivariable statistics are equidistributed either with the triplet
(fix,des,maj), or the pair (fix,maj), where "fix," "des" and "maj" denote the
number of fixed points, the number of descents and the major index,
respectively
- …