Add to ORKGThe purpose of this thesis is to attempt to evaluate the permanent function of a n×n complex matrix with entries aij = θij being a primitive n root of unity. If this matrix is denoted by An then its permanent function is given by per An = [formula omitted] In this thesis the following results are proved. Per An is always an integer; with per An ≡ 0 mod n. If n is even per An = 0. For n odd however, the problem is in general not resolved. It is shown that if n=p² with p a prime, that per An = 0 mod p⁴ and that for any prime n, per An can be narrowed down to be one of a restricted class of numbers.Science, Faculty ofMathematics, Department ofGraduat
AbstractA recent conjecture of Caputo, Carlen, Lieb, and Loss, and, independently, of the author, st...
AbstractIf A is a matrix of order n×(n−2), n⩾3, denote by Ā the n×n matrix whose (i,j)th entry is ze...
AbstractLet A be a fully indecomposable, nonnegative matrix of order n with row sums rl,rn, and let ...
The purpose of this thesis is to attempt to evaluate the permanent function of a n×n complex matrix ...
We sPRThow how to compute the permanent of an n×n integer matrix modulo pk in time nk+O(1) if p=2 an...
We sPRThow how to compute the permanent of an n×n integer matrix modulo pk in time nk+O(1) if p=2 an...
In this paper the author proves some equalities about the permanent of matrices under some condition...
In this paper the author proves some equalities about the permanent of matrices under some condition...
AbstractLet μm be the group of mth roots of unity. In this paper it is shown that if m is a prime po...
Let A be a square matrix over an arbitrary field. The permanent of the matrix A is defined as the al...
Let X be a square matrix of order k over a field F. The permanent of X is given by [Formula omitted...
AbstractFor a complex number q, the q-permanent of an n × n complex matrix A = ((aij)), written perq...
AbstractIf k⩽n, then Gk,n denotes the set of all strictly increasing functions from {1,2,…,k} to {1,...
AbstractLet Λnk be the collection of n × n matrices with nonnegative integer coefficients such that ...
AbstractLet U(n, τ) be the set of all matrices of 0′s and 1′s of order n with exactly τ 0′s. We obta...
AbstractA recent conjecture of Caputo, Carlen, Lieb, and Loss, and, independently, of the author, st...
AbstractIf A is a matrix of order n×(n−2), n⩾3, denote by Ā the n×n matrix whose (i,j)th entry is ze...
AbstractLet A be a fully indecomposable, nonnegative matrix of order n with row sums rl,rn, and let ...
The purpose of this thesis is to attempt to evaluate the permanent function of a n×n complex matrix ...
We sPRThow how to compute the permanent of an n×n integer matrix modulo pk in time nk+O(1) if p=2 an...
We sPRThow how to compute the permanent of an n×n integer matrix modulo pk in time nk+O(1) if p=2 an...
In this paper the author proves some equalities about the permanent of matrices under some condition...
In this paper the author proves some equalities about the permanent of matrices under some condition...
AbstractLet μm be the group of mth roots of unity. In this paper it is shown that if m is a prime po...
Let A be a square matrix over an arbitrary field. The permanent of the matrix A is defined as the al...
Let X be a square matrix of order k over a field F. The permanent of X is given by [Formula omitted...
AbstractFor a complex number q, the q-permanent of an n × n complex matrix A = ((aij)), written perq...
AbstractIf k⩽n, then Gk,n denotes the set of all strictly increasing functions from {1,2,…,k} to {1,...
AbstractLet Λnk be the collection of n × n matrices with nonnegative integer coefficients such that ...
AbstractLet U(n, τ) be the set of all matrices of 0′s and 1′s of order n with exactly τ 0′s. We obta...
AbstractA recent conjecture of Caputo, Carlen, Lieb, and Loss, and, independently, of the author, st...
AbstractIf A is a matrix of order n×(n−2), n⩾3, denote by Ā the n×n matrix whose (i,j)th entry is ze...
AbstractLet A be a fully indecomposable, nonnegative matrix of order n with row sums rl,rn, and let ...