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Oligomorphic permutation groups
 LONDON MATHEMATICAL SOCIETY STUDENT TEXTS
, 1999
"... A permutation group G (acting on a set Ω, usually infinite) is said to be oligomorphic if G has only finitely many orbits on Ω n (the set of ntuples of elements of Ω). Such groups have traditionally been linked with model theory and combinatorial enumeration; more recently their grouptheoretic pro ..."
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A permutation group G (acting on a set Ω, usually infinite) is said to be oligomorphic if G has only finitely many orbits on Ω n (the set of ntuples of elements of Ω). Such groups have traditionally been linked with model theory and combinatorial enumeration; more recently their group
Sequences realized by oligomorphic permutation groups
 J. Integer Seq
, 2000
"... Abstract: The purpose of this paper is to identify, as far as possible, those sequences in the Encyclopedia of Integer Sequences which count orbits of an infinite permutation group acting on nsets or ntuples of elements of the permutation domain. The paper also provides an introduction to the prop ..."
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Abstract: The purpose of this paper is to identify, as far as possible, those sequences in the Encyclopedia of Integer Sequences which count orbits of an infinite permutation group acting on nsets or ntuples of elements of the permutation domain. The paper also provides an introduction
Sequences realized as Parker vectors of oligomorphic permutation groups
 Journal of Integer Sequences 6, (2003) Article 03.1.6
"... The purpose of this paper is to study the Parker vectors (in fact, sequences) of several known classes of oligomorphic groups. The Parker sequence of a group G is the sequence that counts the number of Gorbits on cycles appearing in elements of G. This work was inspired by Cameron’s paper on the se ..."
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The purpose of this paper is to study the Parker vectors (in fact, sequences) of several known classes of oligomorphic groups. The Parker sequence of a group G is the sequence that counts the number of Gorbits on cycles appearing in elements of G. This work was inspired by Cameron’s paper
Oligomorphic clones
 Algebra Universalis
, 2007
"... Abstract. A permutation group on a countably infinite domain is called oligomorphic if it has finitely many orbits of finitary tuples. We define a clone on a countable domain to be oligomorphic if its set of permutations forms an oligomorphic permutation group. There is a close relationship to ωcat ..."
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Abstract. A permutation group on a countably infinite domain is called oligomorphic if it has finitely many orbits of finitary tuples. We define a clone on a countable domain to be oligomorphic if its set of permutations forms an oligomorphic permutation group. There is a close relationship to ω
On the distribution of the length of the longest increasing subsequence of random permutations
 J. Amer. Math. Soc
, 1999
"... Let SN be the group of permutations of 1, 2,...,N. If π ∈ SN,wesaythat π(i1),...,π(ik) is an increasing subsequence in π if i1 <i2 <·· · <ikand π(i1) < π(i2) < ···<π(ik). Let lN (π) be the length of the longest increasing subsequence. For example, if N =5andπis the permutation 5 1 ..."
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Cited by 495 (33 self)
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Let SN be the group of permutations of 1, 2,...,N. If π ∈ SN,wesaythat π(i1),...,π(ik) is an increasing subsequence in π if i1 <i2 <·· · <ikand π(i1) < π(i2) < ···<π(ik). Let lN (π) be the length of the longest increasing subsequence. For example, if N =5andπis the permutation 5 1
Aspects of infinite permutation groups
"... Until 1980, there was no such subgroup as ‘infinite permutation groups’, according to the Mathematics Subject Classification: permutation groups were assumed to be finite. There were a few papers, for example [10, 62], and a set of lecture notes by Wielandt [72], from the 1950s. Now, however, there ..."
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permutation groups); oligomorphic permutation groups (where the relations with other areas such as logic and combinatorics are clearest, and where a number of interesting enumerative questions arise); and the Urysohn space (another case study). I have preceded this with a short section introducing
Praeger, ‘Infinitary versions of the O’Nan–Scott Theorem
 Proc. London Math. Soc
, 1994
"... Various versions are given of an O'NanScott Theorem for infinite primitive permutation groups. For example, if G is a primitive permutation group on a countably infinite set and G has a minimal closed normal subgroup (in the usual topology of pointwise convergence) which in turn has a minimal ..."
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closed normal subgroup, then a natural infinite version of the O'NanScott Theorem holds. This is applied to closed oligomorphic permutation groups. 1.
Permutation group algebras
 J. Alg. Combinatorics
"... We consider the permutation group algebra defined by Cameron and show that if the permutation group has no finite orbits, then no homogeneous element of degree one is a zerodivisor of the algebra. We proceed to make a conjecture which would show that the algebra is an integral domain if, in additio ..."
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We consider the permutation group algebra defined by Cameron and show that if the permutation group has no finite orbits, then no homogeneous element of degree one is a zerodivisor of the algebra. We proceed to make a conjecture which would show that the algebra is an integral domain if
Strange Permutation Representations of Free Groups
"... Certain permutation representations of free groups are constructed by finite approximation. The first is a construction of a cofinitary group with special properties, answering a question of Tim Wall published by Cameron. The second yields, via a method of Kepert and Willis, a totally disconnected l ..."
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Certain permutation representations of free groups are constructed by finite approximation. The first is a construction of a cofinitary group with special properties, answering a question of Tim Wall published by Cameron. The second yields, via a method of Kepert and Willis, a totally disconnected
Results 1  10
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