Classifying Discrete Structures by Their Stabilizers

  • Gilbert LabelleEmail author
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 1125)


Combinatorial power series are formal power series of the form \(\sum c_{n,H}X^n/H \) where, for each n, H runs through subgroups of the symmetric group \(S_n\) and the coefficients \(c_{n,H}\) are complex numbers (or ordinary power series involving some “weight variables”). Such series conveniently encode species of combinatorial (possibly weighted) structures according to their stabilizers (up to conjugacy). We give general lines for expressing these kinds of series – as well as the main operations \((+,\cdot ,\times ,\circ ,d/dX)\) between them – by making use of the GroupTheory package and give suggestions for possible extensions of that package and some other specific procedures such as collect, expand, series, etc. An analysis of multivariable combinatorial power series is also presented.


Discrete structures Stabilizers Combinatorial operations 


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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.LaCIM, Université du Québec à MontréalMontréalCanada

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