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Does there exist an explicit criterion (or a good sufficient condition) for proving that a Vandemonde matrix: $$A(x_1,\dots,x_n):=\left[ \begin{array}{llll}1 & x_1 &\dots& x_1^{n-1}\\ 1 &... 0answers 105 views ### What is wrong with the argument that zero permanent is polynomial? This Lecture summarizes some well known facts about \#P completeness of permanent. Given a CNF formula \phi on n variables, they construct matrix A such that:$$perm(A)=4^{3m} \#SAT(\phi)$$... 0answers 61 views ### Zero as a repeated permanental root for a matrix over a finite field All, Suppose A \in Mat(n, \mathbb{F}_{q}) for q prime, q \geq 5, and n \geq 2^{q-2} . Let \pi_A(x) be the permanental polynomial for A. That is, \begin{equation*} \pi_{A}(x)=per(xI-A). \... 1answer 211 views ### Distribution of the permanent modulo p We know that the order of SL_n({\mathbb F}_p) is$$p^{n(n-1)/2}(p^n-1)(p^{n-1}-1)\cdots(p^2-1).Dividing by p^{n^2}, we deduce the probability that \det takes the value 1 over M_n({\mathbb ... 0answers 82 views ### Does this permanent have a closed form? What is the closed form of this permanent? (similar to the Cauchy determinant) \begin{aligned} f(z_1,z_2,\cdots,z_N,w_1,w_2,\cdots,w_N)=\left[ \small{\begin{matrix} \frac{1}{(z_1-w_1)^2} && \... 0answers 99 views ### Multi-dimensional permanent of structured tensor I am facing the multidimensional permanent $$\text{perm}(W) = \sum_{\sigma, \rho \in S_n} \prod_{j=1}^n W_{j, \sigma_j, \rho_j }$$ of a 3-tensor W_{j,k,l} of ... 1answer 303 views ### About an identity which gives immediate proof of the permanent lemma Let A be a n \times n matrix over field F. Let a_1, \cdots, a_n be the column vectors of A. For any subset S \subseteq [n] = \{1, 2, \cdots, n\}, let a_S = \sum_{i \in S} a_i. Alon's ... 0answers 132 views ### Reduction from permanent to (0,1)-permanent and implication of P \ne NP Valiant shows reduction from counting the solutions of CNF formula F,\#SAT(F) to computing permanent where  Perm(A)= 4^{t(F)}\cdot \#SAT(F) for certain efficiently computable t(F) and matrix ... 0answers 510 views ### Are there any nontrivial near-isometries of the n-dimensional cube? Consider the n-dimensional Hamming cube, C = \{-1,1\}^n. Given an n \times n orthogonal matrix O, I'll measure "how close O is to being an isometry of C" by the following scoring function:... 3answers 2k views ### Silly me & Van der Waerden conjecture So I walked into this very innocent-looking combinatorics problem, and quite soon I ended up with the problem to prove that any doubly stochastic n \times n matrix has a non-zero permanent. Now ... 1answer 235 views ### A generalization of van der Waerden's conjecture I am wondering if the following generalization of van der Waerden's conjecture is true. Suppose A is an n x n non-negative matrix with all column sums equal to 1, and the sum of row i equal to T_i. ... 4answers 331 views ### Permanent identities for special classes of matrices The permanent P(M) of a matrix M of size n is defined to be: P(M) := \sum_{\sigma \in S_n}\prod_{i=1}^n M_{i\sigma(i)} $$If you have a matrix of the form$$ M_{ij} := A_i + B_j  where ...
Is there a practical way to compute the permanent of a large ($91 \times 91$) $(0,1)$ matrix? I have tried to use the matlab function written by Luke Winslow which works great for smaller matrices ...
Let $A(k,n)$ be the set of $\{0,1\}$ matrices of order $n$ with all their line sums equal to $k$. Conjecture number 5 on the list from Minc's book, attributed to Ryser, says that if $A(k,n)$ ...