When is the orbit algebra of a group an integral domain ? Proof of a conjecture of P.J. Cameron

DOI10.1051/ita:2007054zbMath1146.03015arXiv0704.1548OpenAlexW1992923277WikidataQ123352108 ScholiaQ123352108MaRDI QIDQ3514636

Maurice Pouzet

Publication date: 21 July 2008

Published in: RAIRO - Theoretical Informatics and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0704.1548

zbMATH Keywords

permutation grouprelational structureoligomorphic groupsintegral domainorbit algebracounting functionsage algebraenumeration of finite substructures

Mathematics Subject Classification ID

Enumeration in graph theory (05C30) Asymptotic enumeration (05A16) Model theory of finite structures (03C13) Properties of classes of models (03C52) Infinite automorphism groups (20B27)

Related Items (5)

The orbit algebra of an oligomorphic permutation group with polynomial profile is Cohen-Macaulay ⋮ Some relational structures with polynomial growth and their associated algebras. I: Quasi-polynomiality of the profile ⋮ Injective envelopes of transition systems and Ferrers languages ⋮ The morphology of infinite tournaments; application to the growth of their profile ⋮ A survey of homogeneous structures

Cites Work

• Transitivity of permutation groups on unordered sets
• Application d'une propriété combinatoire des parties d'un ensemble aux groupes et aux rélations
• A natural ring basis for the shuffle algebra and an application to group schemes
• Some counting problems related to permutation groups
• Transitivity of finite permutation groups on unordered sets
• On incidence matrices of finite projective and affine spaces
• Growth Rates in Infinite Graphs and Permutation Groups
• Relation Minimale Pour Son Ǎge
• Orbits of Permutation Groups on Unordered Sets, II
• Application de la Notion de Relation Presque‐Enchainable au Denombrement des Restrictions Finies D'une Relation
• On an algebra related to orbit-counting
• A Certain Class of Incidence Matrices
• Ordering by Divisibility in Abstract Algebras
• Sandwiches of ages
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