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The Catalan numbers

by Ira M. Gessel, Guoce Xin , 2004
"... Abstract. 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). When m = 1 they are n twice the Catalan numbers. In this paper, we give a combinatorial interpretation for these ..."
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Abstract. 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). When m = 1 they are n twice the Catalan numbers. In this paper, we give a combinatorial interpretation for these

Catalan numbers

by Frazer Jarvis
"... 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 (b ..."
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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

The Catalan numbers

by unknown authors
"... Abstract. Catalan numbers C(n) = 1 n+1 n enumerate binary trees and Dyck paths. The distribution of paths with respect to their number k of factors is given by ballot numbers B(n, k) = n−k � � n+k n+k n. These integers are known to satisfy simple recurrence, which may be visualised in a “Catalan ..."
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Abstract. Catalan numbers C(n) = 1 n+1 n enumerate binary trees and Dyck paths. The distribution of paths with respect to their number k of factors is given by ballot numbers B(n, k) = n−k � � n+k n+k n. These integers are known to satisfy simple recurrence, which may be visualised in a “Catalan

The Catalan numbers

by unknown authors , 1982
"... Cn = ( 2 n n)/(n + l) belong to the class of advanced counting numbers that appear as naturally and almost as frequently as the binomial coefficients $ due to the extensive variety of combinatorial objects counted by them (see [1]9 [2])« The purpose of this note is to give a combinatorial proof of ..."
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Cn = ( 2 n n)/(n + l) belong to the class of advanced counting numbers that appear as naturally and almost as frequently as the binomial coefficients $ due to the extensive variety of combinatorial objects counted by them (see [1]9 [2])« The purpose of this note is to give a combinatorial proof

Catalan Numbers ∗

by Darrin D. Frey, James A. Sellers
"... In this paper, we consider sequences comprised of n (m − 1)’s and r −1’s (where m ≥ 2) with the sum of each subsequence of the first j terms nonnegative. We will denote the number of such sequences as � � n r m−1. Our goal is to present various results involving � � n r m−1, including an interpret ..."
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In this paper, we consider sequences comprised of n (m − 1)’s and r −1’s (where m ≥ 2) with the sum of each subsequence of the first j terms nonnegative. We will denote the number of such sequences as � � n r m−1. Our goal is to present various results involving � � n r m−1, including

The Catalan numbers Recall the Catalan number

by Vic Reiner, Parabolic Subgroups , 2012
"... V. Reiner Reflection group counting and q-countingOutline The Catalan and parking function family 1 Lecture 1 Things we count What is a finite reflection group? Taxonomy of reflection groups ..."
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V. Reiner Reflection group counting and q-countingOutline The Catalan and parking function family 1 Lecture 1 Things we count What is a finite reflection group? Taxonomy of reflection groups

Divisibility of generalized Catalan numbers

by M. Konvalinka
"... We define a q generalization of weighted Catalan numbers studied by Postnikov and Sagan, and prove a result on the divisibility by p of such ..."
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We define a q generalization of weighted Catalan numbers studied by Postnikov and Sagan, and prove a result on the divisibility by p of such

Moments on Catalan number

by Xin Chen, Jane Wang - J. Math. Anal. Appl
"... Abstract. We give a combinatorial interpretation using lattice paths for the super Catalan number S(m,m+ s) for s ≤ 3 and a separate interpretation for ..."
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Abstract. We give a combinatorial interpretation using lattice paths for the super Catalan number S(m,m+ s) for s ≤ 3 and a separate interpretation for

Catalan Numbers and Random Matrices

by Lawrence Ip, Supervised Alan Edelman , 1999
"... Catalan numbers, the number of ways of pairing n brackets, arise naturally in some random matrix results in the computation of moments of eigenvalue distributions. ..."
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Catalan numbers, the number of ways of pairing n brackets, arise naturally in some random matrix results in the computation of moments of eigenvalue distributions.

Parametric Catalan numbers and Catalan triangles

by Tian-xiao He - Linear Algebra Appl
"... Here presented a generalization of Catalan numbers and Cata-lan triangles associated with two parameters based on the se-quence 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 n ..."
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Here presented a generalization of Catalan numbers and Cata-lan triangles associated with two parameters based on the se-quence 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
Results 1 - 10 of 588