Some new binomial sums related to the Catalan triangle

zbMath1300.05041MaRDI QIDQ405119

Fei Ma, Yidong Sun

Publication date: 4 September 2014

Published in: The Electronic Journal of Combinatorics (Search for Journal in Brave)

Full work available at URL: http://www.combinatorics.org/ojs/index.php/eljc/article/view/v21i1p33

zbMATH Keywords

Catalan numberCatalan triangleballot number

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Combinatorial identities, bijective combinatorics (05A19) Determinants, permanents, traces, other special matrix functions (15A15)

Related Items (7)

Moments on quadratic binomial products ⋮ Generalized Delannoy matrices and their combinatorial properties ⋮ Two infinite families of terminating binomial sums ⋮ Total positivity of Catalan triangle ⋮ Proofs of two conjectures on Catalan triangle numbers ⋮ Combinatorial identities related to \(2 \times 2\) submatrices of recursive matrices ⋮ Triple product sums of Catalan triangle numbers

Uses Software

• OEIS

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Harmonic numbers, Catalan's triangle and mesh patterns
• Combinatorial sums through Riordan arrays
• Combinatorics of Riordan arrays with identical \(A\) and \(Z\) sequences
• Structural properties of Riordan matrices and extending the matrices
• The doubloon polynomial triangle
• Square-bounded partitions and Catalan numbers
• Identities induced by Riordan arrays
• The enumeration of permutations with a prescribed number of ``forbidden patterns
• Matrix identities on weighted partial Motzkin paths
• Multivariate Fuss-Catalan numbers
• Moments on Catalan numbers
• Moments of combinatorial and Catalan numbers
• Factors of binomial sums from the Catalan triangle
• Eplett's identity for renewal arrays
• Catalan numbers, their generalization, and their uses
• The method of creative telescoping
• The Riordan group
• Some more properties of Catalan numbers
• Super ballot numbers
• A Catalan triangle
• A note about the Catalan triangle
• Pascal triangles, Catalan numbers and renewal arrays
• Catalan-like numbers and determinants
• Riordan arrays and combinatorial sums
• Some statistics on Dyck paths
• Taylor expansions for Catalan and Motzkin numbers
• Bijections and the Riordan group
• Several identities in the Catalan triangle
• Generating trees and proper Riordan arrays
• Combinatorial analogues of ad-nilpotent ideals for untwisted affine Lie algebras
• Enumeration via ballot numbers
• A symbolic treatment of Riordan arrays
• Minors of a class of Riordan arrays related to weighted partial Motzkin paths
• Simple proofs of open problems about the structure of involutions in the Riordan group
• New identities in the Catalan triangle
• Proper generating trees and their internal path length
• Some combinatorial arrays generated by context-free grammars
• Some Problems in Combinatorics
• Level generating trees and proper Riordan arrays
• An Occurrence of the Ballot Numbers in Operator Theory
• Counting Arrangements of 1's and -1's

This page was built for publication: Some new binomial sums related to the Catalan triangle