Species on digraphs
type: Item
instance of: scholarly article
title: Species on digraphs
zbMATH Open document ID: 0865.05078
author: Miguel A. Méndez
published in: Advances in Mathematics
publication date: 1997-06-29T00:00:00Z
review text: The author applies the language of Joyal's species to enumeration problems of digraphs using the machinery of coloured species, see, e.g., the author and \textit{O. Nava} [J. Comb. Theory, Ser. A 64, No. 1, 102-129 (1993; Zbl 0787.05095)]. A species over digraphs is defined as a functor from the category of digraphs to the category of finite sets and bijections. Also, a matrix species is defined as an endofunctor of the category of digraphs, and a new set-theoretical operation between such species is introduced. As a result, an enriched version of the MacMahon master theorem is obtained. Other results are a new combinatorial proof of the all minors matrix tree theorem [see, e.g., \textit{S. Chaiken}, SIAM J. Algebraic Discrete Methods 3, 319-329 (1982; Zbl 0495.05018)] and a generalization of the BEST theorem [\textit{T. van Aardenne-Ehrenfest} and \textit{N. G. de Bruijn}, Simon Stevin 28, 203-217 (1951; Zbl 0044.38201)].
reviewed by: Indulis Strazdins
Mathematics Subject Classification ID: 05E99
Mathematics Subject Classification ID: 05C20
Mathematics Subject Classification ID: 15A15
Mathematics Subject Classification ID: 18A10
zbMATH DE Number: 977961
zbMATH Keywords: set operation
zbMATH Keywords: generating function
zbMATH Keywords: enumeration
zbMATH Keywords: digraphs
zbMATH Keywords: coloured species
zbMATH Keywords: matrix species
zbMATH Keywords: MacMahon master theorem
zbMATH Keywords: all minors matrix tree theorem
MaRDI profile type: Publication
full work available at URL: aima.1996.0073
OpenAlex ID: W2073433527
DOI: 10.1006/AIMA.1996.0073
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description: scientific article; zbMATH DE number 977961