منابع مشابه
q-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 کاملCoincidences 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 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 کاملq-Analogs of some congruences involving Catalan numbers
We provide some variations on the Greene-Krammer's identity which involve q-Catalan numbers. Our method reveals a curious analogy between these new identities and some congruences modulo a prime.
متن کاملq, t-Fuß-Catalan numbers for complex reflection groups
In type A, the q, t-Fuß-Catalan numbers Cat n (q, t) can be defined as a bigraded Hilbert series of a module associated to the symmetric group Sn. We generalize this construction to (finite) complex reflection groups and exhibit some nice conjectured algebraic and combinatorial properties of these polynomials in q and t. Finally, we present an idea how these polynomials could be related to some...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 1985
ISSN: 0097-3165
DOI: 10.1016/0097-3165(85)90089-5