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.,

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