Asymptotic results for permutation
                    groups

Pyber, László

doi:10.1090/dimacs/011/14

Cited by 61 publications

(37 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This pattern is unlikely to hold in general; it is plausible that the proportion which are Schurian tends to zero as the number of points increases. Pyber [30] gives some results on the number of subgroups of S n ; it is likely that only a small proportion of these are 2-closed. However, only in special cases such as particular strongly regular graphs do good estimates for the numbers of coherent configurations exist.…”

Section: Some Special Coherent Configurationsmentioning

confidence: 99%

Coherent configurations, association schemes and permutation groups

Cameron¹

2003

Groups, Combinatorics and Geometry

View full text Add to dashboard Cite

Coherent configurations are combinatorial objects invented for the purpose of studying finite permutation groups; every permutation group which is not doubly transitive preserves a non-trivial coherent configuration. However, symmetric coherent configurations have a much longer history, having been used in statistics under the name of association schemes.The relationship between permutation groups and association schemes is quite subtle; there are groups which preserve no non-trivial association scheme, and other groups for which there is not a unique minimal association scheme. This paper gives a brief outline of the theory of coherent configurations and association schemes, and reports on some recent work on the connection between association schemes and permutation groups.

show abstract

Section: Some Special Coherent Configurationsmentioning

confidence: 99%

Coherent configurations, association schemes and permutation groups

Cameron¹

2003

Groups, Combinatorics and Geometry

View full text Add to dashboard Cite

show abstract

“…As complements to this article, the reader may enjoy the surveys [Py1], [Py2], [Py3], [Sh2], [Sh3] on enumerative and probabilistic questions in group theory. The current article uses probabilistic language, but this is just enumeration in disguise.…”

Section: Jason Fulmanmentioning

confidence: 99%

Random matrix theory over finite fields

Fulman

2001

Bull. Amer. Math. Soc.

View full text Add to dashboard Cite

Abstract. The first part of this paper surveys generating functions methods in the study of random matrices over finite fields, explaining how they arose from theoretical need. Then we describe a probabilistic picture of conjugacy classes of the finite classical groups. Connections are made with symmetric function theory, Markov chains, Rogers-Ramanujan type identities, potential theory, and various measures on partitions.

show abstract

“…Recall that e = ⌈b/t⌉ (see (21)), and b = b(H) satisfies the upper bound in (12). In view of (9), (10) and (14) we deduce that there are absolute constants c i such that b(G) ⌈a/r⌉ + ⌈b/t⌉ + 3 c 1 1 ⌊log |Γ|⌋ + c 2 log |P | k⌊log |Γ|⌋ + c 3 log |H| t log |Γ| c 4 log |P | log |Ω| + c 5 k log(|S| ℓ |A ℓ |) t log |Ω| c 6 log |G| log |Ω| as required (the final inequality follows from (19)). …”

Section: Case 22 T >mentioning

confidence: 84%

On Pyber’s base size conjecture

Burness¹,

Seress

2015

Trans. Amer. Math. Soc.

View full text Add to dashboard Cite

Abstract. Let G be a permutation group on a finite set Ω. A subset of Ω is a base for G if its pointwise stabilizer in G is trivial. The base size of G, denoted b(G), is the smallest size of a base. A well known conjecture of Pyber from the early 1990s asserts that there exists an absolute constant c such that b(G) c log |G|/ log n for any primitive permutation group G of degree n. Some special cases have been verified in recent years, including the almost simple and diagonal cases. In this paper, we prove Pyber's conjecture for all non-affine primitive groups.

show abstract

Asymptotic results for permutation groups

Cited by 61 publications

References 0 publications

Coherent configurations, association schemes and permutation groups

Coherent configurations, association schemes and permutation groups

Random matrix theory over finite fields

On Pyber’s base size conjecture

Contact Info

Product

Resources

About