On (+1,−1)-matrices with vanishing permanent
نویسندگان
چکیده
منابع مشابه
On the Permanent of Certain Circulant Matrices
In this paper we rst review the basic computational properties of per-manents, and then address some problems concerning permanents of (0; 1) circulant matrices. In particular we analyze their role at the boundary between computational tractability and intractability, showing that (i) a generic circulant matrix contains large arbitrary submatrices, a fact which casts some doubt on the tractabil...
متن کاملApproximating the Permanent of a Random Matrix with Vanishing Mean
Building upon a recent approach pioneered by Barvinok [4, 5, 7, 8] we present a quasi polynomial time algorithm for approximating the permanent of a typical n×n random matrix with unit variance and vanishing mean μ = (ln lnn)−1/6 to within inverse polynomial multiplicative error. This result counters the common intuition that the difficulty of computing the permanent, even approximately, stems ...
متن کاملPermanent Index of Matrices Associated with Graphs
A total weighting of a graph G is a mapping f which assigns to each element z ∈ V (G)∪E(G) a real number f(z) as its weight. The vertex sum of v with respect to f is φf (v) = ∑ e∈E(v) f(e) + f(v). A total weighting is proper if φf (u) 6= φf (v) for any edge uv of G. A (k, k′)-list assignment is a mapping L which assigns to each vertex v a set L(v) of k permissible weights, and assigns to each e...
متن کاملMaximising the permanent and complementary permanent of (0, 1)-matrices with constant line sum
Let n denote the set of (0; 1)-matrices of order n with exactly k ones in each row and column. Let Ji be such that i = {Ji} and for A∈ n de ne A∈ n−k n by A = Jn − A. We are interested in the matrices in n which maximise the permanent function. Consider the sets M n = {A∈ n: per(A)¿per(B); for all B∈ n}; M k n = {A∈ n: per(A)¿per(B); for all B∈ n}: For k xed and n su ciently large we prove the ...
متن کاملComputing the permanent of (some) complex matrices
where Sn is the symmetric group of permutations of the set {1, . . . , n}. The problem of efficient computation of the permanent has attracted a lot of attention. It is #P -hard already for 0-1 matrices [Va79], but a fully polynomial randomized approximation scheme, based on the Markov Chain Monte Carlo approach, is constructed for all non-negative matrices [J+04]. A deterministic polynomial ti...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1983
ISSN: 0012-365X
DOI: 10.1016/0012-365x(83)90279-0