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1.
Peter J. Cameron 《Designs, Codes and Cryptography》1996,8(1-2):109-133
The main theme of this article is that counting orbitsof an infinite permutation group on finite subsets or tuplesis very closely related to combinatorial enumeration; this pointof view ties together various disparate ``stories'. Among theseare reconstruction problems, the relation between connected andarbitrary graphs, the enumeration of N-free posets, and someof the combinatorics of Stirling numbers. 相似文献
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Kai Wang 《Discrete Mathematics》2019,342(3):888-897
We present formulas to count the set of degree sequences of simple graphs of order , the set of degree sequences of those graphs with no isolated vertices, and the set of degree sequences of those graphs that are -connected for fixed . The formulas all use a function of Barnes and Savage and the associated dynamic programming algorithms all run in time polynomial in and are asymptotically faster than previous known algorithms for these problems. We also show that and are asymptotically equivalent but and as well as and with fixed are asymptotically inequivalent. Finally, we explain why we are unable to obtain the absolute asymptotic orders of these functions from their formulas. 相似文献
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LI Jiongsheng 《中国科学A辑(英文版)》2000,43(1)
An answer is given to a problem proposed by Bannai and Ito for {l,l+s,l+s+t}-sharp permutation group, and the result is used to determine L-sharp groups for L={l,l+1,l+3}and{l,l+2,l+3}. 相似文献
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Jiongsheng Li 《中国科学A辑(英文版)》2000,43(1):22-27
An answer is given to a problem proposed by Bannai and Ito for {I, I + s, I + s + t}-sharp permutation group, and the result is used to determineL-sharp groups for L={I, I + 1, I + 3} and {I, I + 2, I + 3}. 相似文献
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Andrei Asinowski 《Discrete Mathematics》2008,308(20):4745-4762
We define suballowable sequences of permutations as a generalization of allowable sequences. We give a characterization of allowable sequences in the class of suballowable sequences, prove a Helly-type result on sets of permutations which form suballowable sequences, and show how suballowable sequences are related to problems of geometric realizability. We discuss configurations of points and geometric permutations in the plane. In particular, we find a characterization of pairwise realizability of planar geometric permutations, give two necessary conditions for realizability of planar geometric permutations, and show that these conditions are not sufficient. 相似文献
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Mariusz Grech 《Journal of Graph Theory》2009,62(1):26-36
In this article we study the product action of the direct product of automorphism groups of graphs. We generalize the results of Watkins [J. Combin Theory 11 (1971), 95–104], Nowitz and Watkins [Monatsh. Math. 76 (1972), 168–171] and W. Imrich [Israel J. Math. 11 (1972), 258–264], and we show that except for an infinite family of groups Sn × Sn, n≥2 and three other groups D4 × S2, D4 × D4 and S4 × S2 × S2, the direct product of automorphism groups of two graphs is itself the automorphism group of a graph. © 2009 Wiley Periodicals, Inc. J Graph Theory 62: 26–36, 2009 相似文献
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Alexander Hulpke. 《Mathematics of Computation》2000,69(232):1633-1651
The lifting of results from factor groups to the full group is a standard technique for solvable groups. This paper shows how to utilize this approach in the case of non-solvable normal subgroups to compute the conjugacy classes of a finite group.
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Mariusz Grech 《Discrete Mathematics》2010,310(21):2877-2882
We show that with the exception of four known cases: C3, C4, C5, and , all regular permutation groups can be represented as symmetric groups of boolean functions. This solves the problem posed by A. Kisielewicz in the paper [A. Kisielewicz, Symmetry groups of boolean functions and constructions of permutation groups, J. Algebra 199 (1998) 379-403]. A slight extension of our proof yields the same result for semiregular groups. 相似文献
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Mariusz Grech 《Journal of Graph Theory》2011,66(4):303-318
In this article, we improve known results, and, with one exceptional case, prove that when k≥3, the direct product of the automorphism groups of graphs whose edges are colored using k colors, is itself the automorphism group of a graph whose edges are colored using k colors. We have handled the case k = 2 in an earlier article. We prove similar results for directed edge‐colored graphs. © 2010 Wiley Periodicals, Inc. J Graph Theory 66:303‐318, 2011 相似文献
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A discrete group G is amenable if there exists a finitely additive probability measure on G which is invariant under left translations and is defined on all subsets of G. It is proved that if the group is generated by two elements and is amenable then there are words being relators whose most of the consecutive pairs of the letters belong to a certain four-element set of pairs. This fact is applied to reproving non-amenability of a braid group. The same group provides an example showing that such type of condition is not su?cient for amenabilty. 相似文献
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In this paper, we classify finite permutation groups with a transitive abelian subgroup that are almost simple, quasiprimitive and innately transitive, which extend the results of Li and Praeger that is on finite permutation groups with a transitive cyclic subgroup. 相似文献
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In an -permutation group , with a chain and its Dedekind completion, the coincidence of two stabilizer subgroups yields a map from to , and this map commutes with all the elements of G. Roughly speaking, a tying is such a map. We show that the permutations of which commute with the tyings are exactly those in the closure of G in the full automorphism group with respect to the coarse stabilizer topology. We term this closure the gate completion of G, written . We show that each o-primitive component of consists of those permutations of the closure of the corresponding G component which respect the orbits of the points which are "tied" to nonsingleton o-blocks. Finally, we show that any two representations of the same lattice-ordered group which are complete and without dead
segments give rise to the same , and that in this case is the -completion of G.
Received January 29, 1995; accepted in final form March 20, 1996. 相似文献
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In this short note, we focus on self-inverse Sheffer sequences and involutions in the Riordan group. We translate the results of Brown and Kuczma on self-inverse sequences of Sheffer polynomials to describe all involutions in the Riordan group. 相似文献
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Teodor Banica 《Journal of Functional Analysis》2005,224(2):243-280
Associated to a finite graph X is its quantum automorphism group G. The main problem is to compute the Poincaré series of G, meaning the series f(z)=1+c1z+c2z2+? whose coefficients are multiplicities of 1 into tensor powers of the fundamental representation. In this paper we find a duality between certain quantum groups and planar algebras, which leads to a planar algebra formulation of the problem. Together with some other results, this gives f for all homogeneous graphs having 8 vertices or less. 相似文献
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Edward W. Packel 《Mathematical Social Sciences》1980,1(1):93-100
Let F a two-alternative voting rule and GF the subgroup of permutations of the voters under which F is invariant. Group theoretic properties of GF provide information about the voting rule F. In particular, sets of imprimitivity of GF describe the ‘committee decomposition’ structure of F and permutation group transitivity of GF (equipotency) is shown to be closely connected with equal distribution of power among the voters. If equipotency replaces anonymity in the hypotheses of May's theorem, voting rules other than simple majority are possible. By combining equipotency with two additional social choice conditions a new characterization of simple majority rule is obtained. Equipotency is proposed as an important alternative to the more restrictive anonymity as a fairness criterion in social choice. 相似文献
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Let be a graph and let be a group of automorphisms of . The graph is called -normal if is normal in the automorphism group of . Let be a finite non-abelian simple group and let with . In this paper we prove that if every connected pentavalent symmetric -vertex-transitive graph is -normal, then every connected pentavalent symmetric -vertex-transitive graph is -normal. This result, among others, implies that every connected pentavalent symmetric -vertex-transitive graph is -normal except is one of 57 simple groups. Furthermore, every connected pentavalent symmetric -regular graph is -normal except is one of 20 simple groups, and every connected pentavalent -symmetric graph is -normal except is one of 17 simple groups. 相似文献
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We study sharp permutation groups of type {0, k} and observe that, once the isomorphism type of a point stabilizer is fixed, there are only finitely many possibilities for such a permutation group. We then show that a sharp permutation group of type {0, k} in which a point stabilizer is isomorphic to the alternating group on 5 letters must be a geometric group. There is, up to permutation isomorphism, one such permutation group. 相似文献