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Mathematical Notes - A class of matrices is determined for which a Polya transformation of permanents into determinants can be defined. 相似文献
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Let Kn denote the set of all n × n nonnegative matrices whose entries have sum n, and let ϕ be a real function on Kn defined by ϕ (X) = Πni=1Σnj=1xij + Πnj=1Σni=1xij − per X for X = [xij] ϵ Kn. A matrix A ϵ Kn is called a ϕ -maximizing matrix on Kn if ϕ (A) ⩾ ϕ (X) for all X ϵ Kn. It is conjectured that Jn = [1/n]n × n is the unique ϕ-maximizing matrix on Kn. In this note, the following are proved: (i) If A is a positive ϕ-maximizing matrix, then A = Jn. (ii) If A is a row stochastic ϕ-maximizing matrix, then A = Jn. (iii) Every row sum and every column sum of a ϕ-maximizing matrix lies between 1 − √2·n!/nn and 1 + (n − 1)√2·n!/nn. (iv) For any p.s.d. symmetric A ϵ Kn, ϕ (A) ⩽ 2 − n!/nn with equality iff A = Jn. (v) ϕ attains a strict local maximum on Kn at Jn. 相似文献
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If A is a doubly stochastic matrix, it is shown that under certain conditions, there exist i, j such that the matrix obtained by replacing both the ith column of A with their average has a smaller permanent than that of A. A result which is stronger than the Egorychev-Falikman theorem on permanents is also proved. 相似文献
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An identity is stated which gives an expansion in terms of permanents for the reciprocal of the characteristic polynomial of a square matrix. 相似文献
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Henryk Minc 《Linear and Multilinear Algebra》1980,9(1):5-16
An inequality of Johnson and Newman for determinants of real matrices is extended to complex matrices. A related inequality for permanents of real matrices is improved by means of a new rearrangement theorem. 相似文献
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We study the central limit theorem for mixed random permanents. 相似文献
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For random permanents, we obtain an estimate of the rate of convergence in the central limit theorem.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 7, pp. 922–927, July, 1995. 相似文献
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The inequality per(A∘B)⩽ perA perB is verified for nonnegative 2×2 and 3×3 Hermitian matrices, where A∘B is the Hadamard product ofA and B. 相似文献
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It is shown in an elementary way that if A and B are positive semidefinite matrices, then per(A + B) ? per A + per B. The conditions under which equality may occur in this inequality are completely described, and some consequences are given. 相似文献
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We provide explicit formulas for the minors of I–A and for per(I–A) where A is a row stochastic matrix. 相似文献
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Permanents are an effective tool for solving many combinatorial problems about enumeration. The respective theory is well
developed and has numerous applications. In this paper the problem of counting the number of distinct 1-perfect binary codes
is reduced to computing a generalized permanent of a particularly constructed multidimensional matrix. 相似文献
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Let p be a prime > 3. It is shown that no integral circulant of order pk exists with determinant pk+1 . It is also shown that m is the determinant of an integral 9×9 circulant if and only if (m, 3)=l, or m = 0 mod 27. The proof makes use of a criterion which must be satisfied by the difference of two units in the cyclotomic field of level pk . 相似文献
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E. Yu. Kaneva 《Ukrainian Mathematical Journal》1995,47(7):1148-1151
We consider the weak convergence of random permanents under certain conditions.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 7, pp. 1002–1005, July, 1995. 相似文献
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Permanents of matrices with random elements are studied. For random permanents of finitedimensional projection matrices, new limiting results are obtained in different asymptotic schemes. The principal statistical functionals such asU-statistics, symmetric statistics, and others, are represented as functionals of permanent measures.Part of this research was supported by the Fund for Fundamental Researches of Ukrainian State Committee of Science and Technology. 相似文献
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Henryk Minc 《Linear and Multilinear Algebra》1987,21(2):109-148
This is a survey of developments in the theory of permanents during the last quadrennium. It is a sequel to the monograph Permanents and the survey article Theory of Permanents 1978-1981. Many of the significant results obtained during the last four years are described in some detail. The current status of the conjectures and unsolved problems listed in previous surveys is described, and new conjectures proposed during the present period are listed. A comprehensive bibliography is appended. together with a list of addenda to previous bibliographies. Each item on either list is followed by an abstract. 相似文献