منابع مشابه
Catalan structures and Catalan pairs
A Catalan pair is a pair of binary relations (S,R) satisfying certain axioms. These objects are enumerated by the well-known Catalan numbers, and have been introduced in [DFPR] with the aim of giving a common language to most of the structures counted by Catalan numbers. Here, we give a simple method to pass from the recursive definition of a generic Catalan structure to the recursive definitio...
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 کاملThe Catalan simplicial set
The Catalan numbers are well known to be the answer to many different counting problems, and so there are many different families of sets whose cardinalities are the Catalan numbers. We show how such a family can be given the structure of a simplicial set. We show how the low-dimensional parts of this simplicial set classify, in a precise sense, the structures of monoid and of monoidal category...
متن کاملThe Catalan matroid
We show how the set of Dyck paths of length 2n naturally gives rise to a matroid, which we call the “Catalan matroid” Cn. We describe this matroid in detail; among several other results, we show that Cn is self-dual, it is representable over Q but not over finite fields Fq with q ≤ n− 2, and it has a nice Tutte polynomial. We then generalize our construction to obtain a family of matroids, whic...
متن کاملThe Catalan numbers
E. Catalan stated in 1874 that the numbers (2m)! (2n)!/m! n! (m+n)! are integers. When m = 0 these numbers are the middle binomial coefficients ( 2n n ) . When m = 1 they are twice the Catalan numbers. In this paper, we give a combinatorial interpretation for these numbers when m = 2.
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ژورنال
عنوان ژورنال: Indagationes Mathematicae
سال: 2017
ISSN: 0019-3577
DOI: 10.1016/j.indag.2016.08.001