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Orbits of Permutation Groups on Unordered Sets, IV: Homogeneity and Transitivity
Author(s) -
Cameron Peter J.
Publication year - 1983
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-27.2.238
Subject(s) - combinatorics , homogeneous , transitive relation , permutation (music) , permutation group , mathematics , citation , countable set , discrete mathematics , computer science , philosophy , library science , aesthetics
We construct and characterise a 3‐homogeneous but not 2‐primitive permutation group H of countable degree. It has a transitive extension J which is 5‐homogeneous but not 3‐primitive; the number n k ( J ) of orbits of J on k ‐sets is the number of boron trees with k end‐vertices. Some groups related to other classes of trees are also constructed. An application to the growth rate of ( n k ( G )) for primitive groups G is given.
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