Catalan numbers, q-Catalan numbers and hypergeometric series
نویسندگان
چکیده
منابع مشابه
Coincidences of Catalan and Q-catalan Numbers
Let Cn and Cn(q) be the nth Catalan number and the nth q-Catalan number, respectively. In this paper, we show that the Diophantine equation Cn = Cm(q) has only finitely many integer solutions (m,n, q) with m > 1, n > 1, q > 1. Moreover, they are all effectively computable. – To Professor Carl Pomerance on his 65th birthday
متن کاملq-Catalan Numbers
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 form...
متن کاملCatalan numbers
Catalan numbers appear in many places throughout mathematics, and are a fairly frequent subject for articles in this magazine. Indeed, a very nice introduction to their properties was given in this magazine by Vun and Belcher [3], and a historical account of their discovery in Chinese mathematics (before Catalan!) has also appeared in a recent article by Larcombe [1]. The article by Vun and Bel...
متن کاملA Filtration of (q,t)-catalan Numbers
Using the operator ∇ of F. Bergeron, Garsia, Haiman and Tesler [2] acting on the k-Schur functions [15, 16, 17] indexed by a single column has a coefficient in the expansion which is an analogue of the (q, t)-Catalan number with a level k. When k divides n we conjecture a representation theoretical model in this case such that the graded dimensions of the module are the coefficients of the (q, ...
متن کاملParametric Catalan Numbers and Catalan Triangles
Here presented a generalization of Catalan numbers and Catalan triangles associated with two parameters based on the sequence characterization of Bell-type Riordan arrays. Among the generalized Catalan numbers, a class of large generalized Catalan numbers and a class of small generalized Catalan numbers are defined, which can be considered as an extension of large Schröder numbers and small Sch...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 1987
ISSN: 0097-3165
DOI: 10.1016/0097-3165(87)90033-1