On the symmetry and asymmetry of combinatorial structures

DOI10.1016/0304-3975(93)90300-IzbMath0784.05008MaRDI QIDQ688675

Gilbert Labelle

Publication date: 13 December 1993

Published in: Theoretical Computer Science (Search for Journal in Brave)

zbMATH Keywords

symmetric grouptreesasymmetric index seriescycle index seriesspecies of structures

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15)

Related Items (11)

A shifted asymmetry index series ⋮ On a generalization of index series of species ⋮ Trees, arborescences, and symmetric square roots ⋮ The plethystic inverse of a formal power series ⋮ Plane trees and Shabat polynomials ⋮ The generic \(q\)-enumeration of a species: Existence and computing method ⋮ Enumeration of (uni- or bicolored) plane trees according to their degree distribution ⋮ Regularity in Weighted Graphs: A Symmetric Function Approach ⋮ Counting asymmetric enriched trees ⋮ Index series and \(q\)-series ⋮ Even permutations and oriented sets: their shifted asymmetry index series

Uses Software

• Maple
• MACSYMA

Cites Work

• Index series and \(q\)-series
• Dérivées directionnelles et développements de Taylor combinatoires. (Directional derivatives and combinatorial Taylor expansions)
• The number of homeomorphically irreducible trees, and other species
• Combinatorial proofs of some limit formulas involving orthogonal polynomials
• Combinatorial resolution of systems of differential equations. IV: Separation of variables
• Une approche combinatoire pour l'itération de Newton-Raphson
• On combinatorial differential equations
• Plethysm, categories and combinatorics
• Une combinatoire du pléthysme. (Combinatorics of plethysm)
• On the generalized iterates of Yeh's combinatorial \({\mathbb{K}}\)-species
• Some combinatorics of the hypergeometric series
• A combinatorial outlook on symmetric functions
• The relation between Burnside rings and combinatorial species
• Combinatorial proofs of symmetry formulas for the generalized hypergeometric series
• Congruences derived from group action
• Une nouvelle demonstration combinatoire des formules d'inversion de Lagrange
• Une théorie combinatoire des séries formelles
• A combinatorial approach to nonlinear functional expansions: An introduction with an example
• Computation of the expected number of leaves in a tree having a given automorphism, and related topics
• The functorial composition of species, a forgotten operation
• On asymmetric structures
• Counting asymmetric enriched trees
• Hereditarily finite sets and identity trees
• Lagrange inversion for species
• The number of trees
• The Combinatorics of Laguerre, Charlier, and Hermite Polynomials
• On Combinatorial Structures Kept Fixed by the Action of a Given Permutation
• Counting Patterns with a Given Automorphism Group
• Baxter algebras and combinatorial identities. II
• Enumeration of non-separable graphs
• [https://portal.mardi4nfdi.de/wiki/Publication:5731810 On the foundations of combinatorial theory I. Theory of M�bius Functions]
• Functional equations for data structures
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