共查询到10条相似文献,搜索用时 0 毫秒
1.
K.W. Johnson 《Journal of Combinatorial Theory, Series A》2010,117(6):790-798
Finite simple, unipotent Bol loops have recently been identified and constructed using group theory. However, the purely group-theoretical constructions of the actual loops are indirect, somewhat arbitrary in places, and rely on computer calculations to a certain extent. In the spirit of revisionism, this paper is intended to give a more explicit combinatorial specification of the smallest simple, unipotent Bol loop, making use of concepts from projective geometry and quasigroup theory along with the group-theoretical background. The loop has dual permutation representations on the projective line of order 5, with doubly stochastic action matrices. 相似文献
2.
3.
For square, semipositive matrices A (Ax>0 for some x>0), two (nonnegative) equilibrants e(A) and E(A) are defined. Our primary goal is to develop theory from which each may be calculated. To this end, the collection of semipositive matrices is partitioned into three subclasses for each equilibrant, and a connection to those matrices that are scalable to doubly stochastic matrices is made. In the process a certain matrix/vector equation that is related to scalability of a matrix to one with line sums 1 is derived and discussed. 相似文献
4.
《代数通讯》2013,41(3):1253-1270
Abstract Let G a simple group of type 2 B 2(q) or 2 G 2(q), where q is an odd power of 2 or 3, respectively. The main goal of this paper is to determine the multiplicity free permutation representations of G and A ≤ Aut(G) where A is a subgroup containing a copy of G. Let B be a Borel subgroup of G. If G = 2 B 2(q) we show that there is only one non-trivial multiplicity free permutation representation, namely the representation of G associated to the action on G/B. If G = 2 G 2(q) we show that there are exactly two such non-trivial representations, namely the representations of G associated to the action on G/B and the action on G/M, where M = UC with U the maximal unipotent subgroup of B and C the unique subgroup of index 2 in the maximal split torus of B. The multiplicity free permutation representations of A correspond to the actions on A/H where H is isomorphic to a subgroup containing B if G = 2 B 2(q), and containing M if G = 2 G 2(q). The problem of determining the multiplicity free representations of the finite simple groups is important, for example, in the classification of distance-transitive graphs. 相似文献
5.
PSN is a fast forward permutation if for each m the computational complexity of evaluating Pm(x) is small independently of m and x. Naor and Reingold constructed fast forward pseudorandom cycluses and involutions. By studying the evolution of permutation graphs, we prove that the number of queries needed to distinguish a random cyclus from a random permutation in SN is Θ(N) if one does not use queries of the form Pm(x), but is only Θ(1) if one is allowed to make such queries. We construct fast forward permutations which are indistinguishable from random permutations even when queries of the form Pm(x) are allowed. This is done by introducing an efficient method to sample the cycle structure of a random permutation, which in turn solves an open problem of Naor and Reingold. 相似文献
6.
Toshiyuki Kobayashi 《Acta Appl Math》2004,81(1):129-146
We analyze the criterion of the multiplicity-free theorem of representations [5, 6] and explain its generalization. The criterion is given by means of geometric conditions on an equivariant holomorphic vector bundle, namely, the visibility of the action on a base space and the multiplicity-free property on a fiber.Then, several finite-dimensional examples are presented to illustrate the general multiplicity-free theorem, in particular, explaining that three multiplicity-free results stem readily from a single geometry in our framework. Furthermore, we prove that an elementary geometric result on Grassmann varieties and a small number of multiplicity-free results give rise to all the cases of multiplicity-free tensor product representations of GL(n,C), for which Stembridge [12] has recently classified by completely different and combinatorial methods. 相似文献
7.
In this paper, we compute all the moments of the real Wishart distribution. To do so, we use the Gelfand pair (S2k,H), where H is the hyperoctahedral group, the representation theory of H and some techniques based on graphs. 相似文献
8.
The notion of a generalized Camina-Frobenius pair is extended to reality-based algebras, and a construction that characterizes such pairs is given. Zero-product sets are defined, and a best-possible upper bound on their size is proved and related to Camina-Frobenius pairs. It is shown that there exist commutative reality-based algebras with zero-product sets and, hence, no degree map, of every dimension at least 4. All such 4-dimensional algebras are constructed explicitly. 相似文献
9.
Hans-Joachim Baues 《K-Theory》1997,11(3):259-285
A category of homotopy pairs is characterised by a cohomology class which generalizes the notion of Toda bracket. Explicit computations of such cohomology classes are described. 相似文献
10.
Frank Uhlig 《Linear and Multilinear Algebra》2013,61(7):954-969
By a theorem of Frobenius (F.G. Frobenius, Über die mit einer Matrix vertauschbaren Matrizen, Sitzungsberichte der Königlich Preußischen Akademie der Wissenschaften zu Berlin (1910), pp. 3–15 (also in Gesammelte Abhandlungen, Band 3, Springer 1968. pp. 415–427)), every matrix A n,n over any field 𝔽 is the product of two symmetric ones. Using the algorithm of Huang and Nong (J. Huang and L. Nong, An iterative algorithm for solving finite-dimensional linear operator equations T(x)?=?f with applications, Linear Algebra Appl. 432 (2010), pp. 1176–1188) for linear systems, we develop an algorithm to compute a symmetric matrix S?=?S T ?∈?𝔽 n,n for which SA is symmetric for any given square matrix A?∈?𝔽 n,n where 𝔽?=?? or ?. The algorithm is implemented and tested in MATLAB. 相似文献