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480
The permutation action of finite symplectic groups of odd characteristic on their standard modules
 J. Algebra
"... Abstract. Motivated by the incidence problems between points and flats of a symplectic polar space, we study a large class of submodules of the space of functions on the standard module of a finite symplectic group of odd characteristic. Our structure results on this class of submodules allow us to ..."
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Cited by 6 (4 self)
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Abstract. Motivated by the incidence problems between points and flats of a symplectic polar space, we study a large class of submodules of the space of functions on the standard module of a finite symplectic group of odd characteristic. Our structure results on this class of submodules allow us to determine the pranks of the incidence matrices between points and flats of the symplectic polar space. In particular, we give an explicit formula for the prank of the incidence matrix between the points and lines of the symplectic generalized quadrangle W(3, q), where q is an odd prime power. Combined with the earlier results of Sastry and Sin on the 2rank of W(3, 2 t), it completes the determination of the pranks of W(3, q). 1.
Universal equivalence relations on XN generated by permutation actions of countable subgroups of S∞
, 2013
"... Let S ∞ be the group of all permutations of N and X be a standard Borel space. Then the space XN of functions from N to X is a standard Borel space, and S ∞ acts on this space by permutation where given x ∈ XN and g ∈ S∞, g · x(n) = x(g−1(n)). Given any countable subgroup G of S∞, we can likewise r ..."
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Let S ∞ be the group of all permutations of N and X be a standard Borel space. Then the space XN of functions from N to X is a standard Borel space, and S ∞ acts on this space by permutation where given x ∈ XN and g ∈ S∞, g · x(n) = x(g−1(n)). Given any countable subgroup G of S∞, we can likewise
The permutation action of the symmetric group S5 on C 5 preserves the hyperplane SOLVING THE QUINTIC BY ITERATION IN THREE DIMENSIONS
, 1999
"... Abstract. The requirement for solving a polynomial is a means of breaking its symmetry, which in the case of the quintic, is that of the symmetric group S5. Descending from its fivedimensional linear permutation representation is a threedimensional projective action. A mapping of complex projectiv ..."
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Abstract. The requirement for solving a polynomial is a means of breaking its symmetry, which in the case of the quintic, is that of the symmetric group S5. Descending from its fivedimensional linear permutation representation is a threedimensional projective action. A mapping of complex
Permutation Statistics of Indexed Permutations
, 1994
"... The definitions of descent, excedance, major index, inversion index and Denert's statistic for the elements of the symmetric group S d are generalized to indexed permutations, i.e. the elements of the group S n d := Z n o S d , where o is wreath product with respect to the usual action of S d ..."
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Cited by 51 (2 self)
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The definitions of descent, excedance, major index, inversion index and Denert's statistic for the elements of the symmetric group S d are generalized to indexed permutations, i.e. the elements of the group S n d := Z n o S d , where o is wreath product with respect to the usual action
Permutation Groups
, 2009
"... The theory of permutation groups is essentially the theory of symmetry for mathematical and physical systems. It therefore has major impact in diverse areas of mathematics. Twentiethcentury permutation group theory focused on the theory of finite primitive permutation groups, and this theory contin ..."
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changed substantially. The classification of finite simple groups has had many applications, many of these through thorough investigation of relevant permutation actions. This in turn led to invigoration of the subject of permutation groups, with interesting new questions arising and techniques developed
Permutation Branes
"... Abstract Nfold tensor products of a rational CFT carry an action of the permutation group SN. These automorphisms can be used as gluing conditions in the study of boundary conditions for tensor product theories. We present an ansatz for such permutation boundary states and check that it satisfies t ..."
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Cited by 33 (1 self)
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Abstract Nfold tensor products of a rational CFT carry an action of the permutation group SN. These automorphisms can be used as gluing conditions in the study of boundary conditions for tensor product theories. We present an ansatz for such permutation boundary states and check that it satisfies
ACTIONS ON PERMUTATIONS AND UNIMODALITY OF DESCENT POLYNOMIALS
, 2006
"... We study an action (the SWGaction) on permutations due to Shapiro, Woan and Getu and use it to prove that the descent generating polynomial of certain sets of permutations has a nonnegative expansion in the basis {ti(1 + t) n−1−2i} ⌊(n−1)/2⌋ i=0. This property implies symmetry and unimodality. We ..."
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Cited by 13 (1 self)
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We study an action (the SWGaction) on permutations due to Shapiro, Woan and Getu and use it to prove that the descent generating polynomial of certain sets of permutations has a nonnegative expansion in the basis {ti(1 + t) n−1−2i} ⌊(n−1)/2⌋ i=0. This property implies symmetry and unimodality. We
Arc permutations
 J. Algebraic Combin
"... Arc permutations and unimodal permutations were introduced in the study of triangulations and characters. This paper studies combinatorial properties and structures on these permutations. First, both sets are characterized by pattern avoidance. It is also shown that arc permutations carry a natura ..."
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Cited by 5 (3 self)
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natural affine Weyl group action, and that the number of geodesics between a distinguished pair of antipodes in the associated Schreier graph, as well as the number of maximal chains in the weak order on unimodal permutations, are both equal to twice the number of standard Young tableaux of shifted
Results 1  10
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480