Result: Catalan-like Numbers and Determinants: Catalan-like numbers and determinants
Title:
Catalan-like Numbers and Determinants: Catalan-like numbers and determinants
Authors:
Source:
Journal of Combinatorial Theory, Series A. 87:33-51
Publisher Information:
Elsevier BV, 1999.
Publication Year:
1999
Subject Terms:
Exact enumeration problems, generating functions, 0102 computer and information sciences, 01 natural sciences, Motzkin numbers, Theoretical Computer Science, Hankel matrices, generating function, Computational Theory and Mathematics, Other combinatorial number theory, recursion, Discrete Mathematics and Combinatorics, Catalan numbers, 0101 mathematics, Combinatorial aspects of matrices (incidence, Hadamard, etc.)
Document Type:
Academic journal
Article
File Description:
application/xml
Language:
English
ISSN:
0097-3165
DOI:
10.1006/jcta.1998.2945
Access URL:
Rights:
Elsevier Non-Commercial
Accession Number:
edsair.doi.dedup.....b32dec7b84e765ef1e5c15f6c8245102
Database:
OpenAIRE
Further Information
The Catalan numbers play a central role in enumerations. They can be defined by recursion but also via so-called Hankel matrices. The Motzkin numbers are defined by a very similar recursion, and Aigner also found a description using Hankel matrices. Both types of numbers are involved in several classical formulae with binomial coefficients (and with each other). This paper introduces the so-called Catalan-like numbers which share these common features. The Catalan and Motzkin numbers are special cases of the Catalan-like numbers. General recursions, binomial identities and a generating function are determined. Catalan-like numbers can be applied in enumerating paths or rooted trees, for example.