منابع مشابه
Eulerian-Catalan Numbers
We show that the Eulerian-Catalan numbers enumerate Dyck permutations. We provide two proofs for this fact, the first using the geometry of alcoved polytopes and the second a direct combinatorial proof via an Eulerian-Catalan analogue of the Chung-Feller theorem.
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 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 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...
متن کاملMultivariate Fuss-Catalan numbers
are integers that appear in many combinatorial problems. These numbers first arose in the work of Catalan as the number of triangulations of a polygon by mean of nonintersecting diagonals. Stanley [13, 14] maintains a dynamic list of exercises related to Catalan numbers, including (at this date) 127 combinatorial interpretations. Closely related to Catalan numbers are ballot numbers. Their name...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2011
ISSN: 1077-8926
DOI: 10.37236/674