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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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