Matrix representation for combinatorics
type: Item
instance of: scholarly article
title: Matrix representation for combinatorics
zbMATH Open document ID: 0548.05004
DOI: 10.1016/0097-3165(84)90037-2
author: John G. Kemeny
published in: Journal of Combinatorial Theory. Series A
publication date: 1984-01-01T00:00:00Z
review text: Many combinatorial quantities have natural representations in terms of denumerably infinite matrices. For example, the matrix \(B=(B_{ij})\), \(i,j=0,1,2,..\). where \(B_{ij}=\left( \begin{matrix} i\\ j\end{matrix} \right)\) represents the binomial coefficients, and if \(b_ k\) is the k-th Bernoulli number the infinite column vector \(b=(b_ k)\), \(k=0,1,2,..\). represents the Bernoulli numbers. By exploiting this idea together with some algebra of denumerably matrices, the author provides a simplification and unification of some traditional results as well as a method of discovery and proof of combinatorial identities. The key concept to his approach is that of the derivative of a denumerably infinite matrix.
Mathematics Subject Classification ID: 05A19
Mathematics Subject Classification ID: 05A10
Mathematics Subject Classification ID: 05A15
zbMATH DE Number: 3873333
zbMATH Keywords: representation of combinatorial quantities
zbMATH Keywords: denumerably infinite matrices
zbMATH Keywords: derivative
reviewed by: Joel V. Brawley
MaRDI profile type: Publication
full work available at URL: 0097-3165(84)90037-2
OpenAlex ID: W2005208814
cites work: Recursive matrices and umbral calculus
cites work: Q4769056
cites work: Q4093447
Recommended article: Q4388723
Recommended article: Combinatorial matrix theory
Recommended article: Combinatorial Matrix Theory
Recommended article: Q4517538
Recommended article: A combinatorial approach to matrix algebra
Recommended article: Q5484517
Recommended article: Matrices with Integer Elements in Combinatorial Investigations
Recommended article: Q3204477
Recommended article: Q3525700
description: scientific article; zbMATH DE number 3873333