Related papers: An update on a few permanent conjectures

We prove a logical implication between two old conjectures stated by Bapat and Sunder about the permanent of positive semidefinite matrices. Although Drury has recently disproved both conjectures, this logical implication yields a…

We survey the impact of Lieb's influential paper "Proofs of some conjectures on permanents" [J. Math. Mech. 16 1966, 127-134], which introduced the famous permanental dominance conjecture. This conjecture has defied all attacks for over…

In this paper we investigate the permanent of $(-1,1)$-matrices over fields of zero characteristics and our main goal is to provide a sharp upper bound for the value of the permanent of such matrices depending on matrix rank, solving Wang's…

In this note we settle two open problems in the theory of permanents by using recent results from other areas of mathematics. Bapat conjectured that certain quotients of permanents, which generalize symmetric function means, are concave. We…

In this paper we provide an identity between determinant and generalized matrix function. Also, a criterion of positive semi-definite matrices affirming the permanent dominant conjecture is given. As a consequence, infinitely many infinite…

The permanent-on-top conjecture states that the largest eigenvalue of the Schur power matrix of a positive semi-definite Hermitian matrix H is per(H). A counterexample has been found with the help of computers, but here, I present another…

In this paper we give the absolutely new proof of a conjecture of R.F.Scott(1881) on the permanent of a Cauchy matrix $\ls \frac{1}{x_i-y_j} \rs_{1 \leqslant i,j \leqslant n},$ where $x_1, ..., x_n$ and $y_1, ..., y_n$ are the distinct…

The permanent of a multidimensional matrix is the sum of products of entries over all diagonals. By Minc's conjecture, there exists a reachable upper bound on the permanent of 2-dimensional (0,1)-matrices. In this paper we obtain some…

We formulate conjectures regarding the maximum value and maximizing matrices of the permanent and of diagonal products on the set of stochastic matrices with bounded rank. We formulate equivalent conjectures on upper bounds for these…

We prove a conjecture due to Wanless about the permanent of Hadamard matrices in the particular case of Sylvester-Hadamard matrices. Namely we show that for all n greater or equal to 2, the dyadic valuation of the permanent of the…

We show that the permanent of a matrix is a linear combination of determinants of block diagonal matrices which are simple functions of the original matrix. To prove this, we first show a more general identity involving \alpha-permanents:…

Let $M_{n}$ denote a random symmetric $n\times n$ matrix, whose entries on and above the diagonal are i.i.d. Rademacher random variables (taking values $\pm 1$ with probability $1/2$ each). Resolving a conjecture of Vu, we prove that the…

Let $R$ be a commutative additively idempotent semiring. In this paper, some properties and characterizations for permanents of matrices over $R$ are established, and several inequalities for permanents are given. Also, the adjiont matrices…

In this paper we discuss minimal primes over permanental ideals of generic matrices. We give a complete list of the minimal primes over ideals of 3 x 3 permanents of a generic matrix, and show that there are monomials in the ideal of…

Expressions involving the product of the permanent with the (n-1)th power of the determinant of a matrix of indeterminates, and of (0,1)-matrices, are shown to be related to two conjectures that extend the Alon-Tarsi Latin square conjecture…

We prove an identity relating the permanent of a rank $2$ matrix and the determinants of its Hadamard powers. When viewed in the right way, the resulting formula looks strikingly similar to an identity of Carlitz and Levine, suggesting the…

In this paper, we give some determinantal and permanental representations of Generalized Lucas Polynomials by using various Hessenberg matrices, which are general form of determinantal and permanental representations of ordinary Lucas and…

It is well-known that the evaluation of the permanent of an arbitrary $(-1,1)$-matrix is a formidable problem. Ryser's formula is one of the fastest known general algorithms for computing permanents. In this paper, Ryser's formula has been…

In this paper, it is shown that $\alpha$-permanent in algebra is closely related to loop soup in probability. We give explicit expansions of $\alpha$-permanents of the block matrices obtained from matrices associated to $*$-forests, which…

In the year 1982, John Chollet conjectured that, for any pair of $n\times n$ positive semidefinite matrices $A,B$, $per(A)\cdot per(B)\geq per(A\circ B)$, where $A\circ B$ is the Hardamard product of $A$ and $B$. This conjecture was proved…