Symmetric function means and permanents
نویسندگان
چکیده
منابع مشابه
Inequalities for symmetric means
We study Muirhead-type generalizations of families of inequalities due to Newton, Maclaurin and others. Each family is defined in terms of a commonly used basis of the ring of symmetric functions in n variables. Inequalities corresponding to elementary symmetric functions and power sum symmetric functions are characterized by the same simple poset which generalizes the majorization order. Some ...
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chapter one is devoted to a moderate discussion on preliminaries, according to our requirements. chapter two which is based on our work in (24) is devoted introducting weighted semigroups (s, w), and studying some famous function spaces on them, especially the relations between go (s, w) and other function speces are invesigated. in fact this chapter is a complement to (32). one of the main fea...
15 صفحه اولApproximating Permanents and Hafnians
We prove that the logarithm of the permanent of an n×n real matrix A and the logarithm of the hafnian of a 2n×2n real symmetric matrix A can be approximated within an additive error 1 ≥ ε > 0 by a polynomial p in the entries of A of degree O(lnn− lnε) provided the entries ai j of A satisfy δ ≤ ai j ≤ 1 for an arbitrarily small δ > 0, fixed in advance. Moreover, the polynomial p can be computed ...
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1. Results. It is well known [2] that if A and B are n and msquare matrices respectively then (1) det(^ ® B) = (det(A))m(det(B))» where A®B is the tensor or direct product of A and B. By taking absolute values on both sides of (1) we can rewrite the equality as (2) I det(4 B) |2 = (det(4^*))'»(det(73*P))«, where A* is the conjugate transpose of A. The main result is a direct extension of (2...
متن کاملInequalities for the gamma function with applications to permanents
The best known upper bound on the permanent of a 0-1 matrix relies on the knowledge of the number of nonzero entries per row. In certain applications only the total number of nonzero entries is known. In order to derive bounds in this situation we prove that the function f : (?1; 1) ! R, deened by f(x) := log ?(x+1) x , is concave, strictly increasing and satisses an analogue of the famous Bohr...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1993
ISSN: 0024-3795
DOI: 10.1016/0024-3795(93)90494-9