q-Catalan Numbers

نویسندگان

  • J. Fürlinger
  • Josef Hofbauer
چکیده

q-analogs of the Catalan numbers c', = (I/(n + I))($) are studied from the viewpoint of Lagrange inversion. The first, due to Carhtz, corresponds to the Andrews-Gessel-Garsia q-Lagrange inversion theory, satisfies a nice recurrence relation and counts inversions of Catalan words. The second, tracing back to Mac Mahon, arise from Krattenthaler's and Gessel and Stanton's q-Lagrange inversion formula, have a nice explicit formula and enumerate the major index. Finally a joint generalization is given which includes also the Polya-Gessel q-Catalan numbers.

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عنوان ژورنال:
  • J. Comb. Theory, Ser. A

دوره 40  شماره 

صفحات  -

تاریخ انتشار 1985