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The proportion of fixed-point-free elements of a transitive permutation group
, 1993In 1990 Hendrik W. Lenstra, Jr. asked the following question: if G is a transitive permutation group of degree n and A is the set of elements of G that move every letter, then can one find a lower bound (in terms of n) for f(G) = |A|/|G|?
N. Boston +6 more
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, 1990
Local chirality and prochirality are discussed by integrating point-group and permutation-group theories. Thereby, a compound of G symmetry is considered to consist of several orbits that are subject to coset representations (CRs).
S. Fujita
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Local chirality and prochirality are discussed by integrating point-group and permutation-group theories. Thereby, a compound of G symmetry is considered to consist of several orbits that are subject to coset representations (CRs).
S. Fujita
semanticscholar +1 more source
A Necessary Condition for Transitivity of a Finite Permutation Group
, 1988Suppose the group G is generated by permutations gvg2,...,g, acting on a set CI of size n, such that 8182--8, ' s the identity permutation. If the generator gt has exactly ci cycles (for 1 ^ / < s), and G is transitive on Ci, then n(s—2)—YJ'(-I c, + 2 is
M. Conder, J. McKay
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Direct evaluation of spin representation matrices and ordering of permutation‐group elements
, 1986A direct and general method is presented for constructing the orthogonal spin representation matrices (irreps) of the permutation group corresponding to the Yammanouchi-Kotani coupling scheme.
S. Rettrup
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Permutation polynomials and primitive permutation groups
Archiv der Mathematik, 1991By STEPSEN D. COHEN 1. Introduction. We present here progress that has been made through the application of the theory of primitive permutation groups to the conjecture of L. Carlitz (1966) on the non-existence of permutation polynomials of even degree over a finite field Fr of odd order q = p~.
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1999
Permutation groups are one of the oldest topics in algebra. However, their study has recently been revolutionised by new developments, particularly the classification of finite simple groups, but also relations with logic and combinatorics, and importantly, computer algebra systems have been introduced that can deal with large permutation groups.
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Permutation groups are one of the oldest topics in algebra. However, their study has recently been revolutionised by new developments, particularly the classification of finite simple groups, but also relations with logic and combinatorics, and importantly, computer algebra systems have been introduced that can deal with large permutation groups.
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1993
The theory of finite permutation groups is the oldest branch of group theory, many parts of it having been developed in the nineteenth century. However, despite its antiquity, the subject continues to be an active field of investigation.
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The theory of finite permutation groups is the oldest branch of group theory, many parts of it having been developed in the nineteenth century. However, despite its antiquity, the subject continues to be an active field of investigation.
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Permutation Groups and Group Actions
2015A useful paradigm for discussing a group is to regard it as acting as a group of permutations of some set. The power of this point of view derives from the flexibility one has in choosing the set being acted on. Odd and even finitary permutations, the cycle notation, orbits, the basic relation between transitive actions and actions on cosets of a ...
David Surowski, Ernest E. Shult
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