Contemporary Mathematics, vol. 254, q-Series from a Contemporary Perspective,
p. 141-156 [AMS-IMS-SIAM Joint Summer Research Conference on q-series, Combinatorics, and
Computer Algebra, in honor of Richard Askey, June 21-25, 1998,
Mount Holyoke College, South Hadley, MA;
Mourad E.H. Ismail, Dennis W. Stanton, eds.], 2000, Providence, Amer. Math. Soc.
Dominique Foata and Guo Niu Han
Word straightening and q-Eulerian Calculus
Abstract.
This paper contains a new description of the straightening algorithm for pairs
of finite words called circuits. The commutation rule underlying the
straightening algorithm that keeps invariant a specific word bivariate
statistic, is fully characterized. A methodology is developed that makes
possible the calculation of the bivariate generating function for that pair of
statistics. That generating function appears to be a generalized form of the
classical q-Eulerian polynomial.
foata@math.u-strasbg.fr, guoniu@math.u-strasbg.fr
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