Related papers: A permanent formula for the Jones polynomial

The colored Jones polynomial is a knot invariant that plays a central role in low dimensional topology. We give a simple and an efficient algorithm to compute the colored Jones polynomial of any knot. Our algorithm utilizes the walks along…

We present a finite-order system of recurrence relations for a permanent of circulant matrices containing a band of k any-value diagonals on top of a uniform matrix (for k = 1, 2, and 3) as well as the method for deriving such recurrence…

We present numerically exact continuous-time Quantum Monte Carlo algorithm for fermions with a general non-local in space-time interaction. The new determinantal grand-canonical scheme is based on a stochastic series expansion for the…

A real square matrix is Perron-like if it has a real eigenvalue $s$, called the principal eigenvalue of the matrix, and $\mbox{Re}\,\mu<s$ for any other eigenvalue $\mu$. Nonnegative matrices and symmetric ones are typical examples of this…

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 graphical realization of a given degree sequence and given partition adjacency matrix simultaneously is a relevant problem in data driven modeling of networks. Here we formulate common generalizations of this problem and the Exact…

We give an explicit formula for the Jones polynomial of any rational link in terms of the denominators of the canonical continued fraction of the slope of the given rational link.

Let $\mathcal A$ be an $\mathbb F$-algebra and $\omega \in \mathcal A\langle x_1, \ldots, x_m \rangle$ which defines a map $\mathcal A^m \rightarrow \mathcal A$ by evaluation, called a polynomial map with constant. We consider $\mathcal {A}…

We study Schur Q-polynomials evaluated on a geometric progression, or equivalently q-enumeration of marked shifted tableaux, seeking explicit formulas that remain regular at q=1. We obtain several such expressions as multiple basic…

A hierarchy of matrix-valued polynomials which generalize the Jacobi polynomials is found. Defined by a Rodrigues formula, they are also products of a sequence of differential operators. Each class of polynomials is complete, satisfies a…

We study the class of polynomials whose Hessians evaluated at any point of a closed convex cone have Lorentzian signature. This class is a generalization to the remarkable class of Lorentzian polynomials. We prove that hyperbolic…

We introduce an efficient numerical implementation of a Markov Chain Monte Carlo method to sample a probability distribution on a manifold (introduced theoretically in Zappa, Holmes-Cerfon, Goodman (2018)), where the manifold is defined by…

We prove that the logarithm of the permanent of an nxn real matrix A and the logarithm of the hafnian of a 2nx2n real symmetric matrix A can be approximated within an additive error 1 > epsilon > 0 by a polynomial p in the entries of A of…

We describe the minimal free resolution of the ideal of $2 \times 2$ subpermanents of a $2 \times n$ generic matrix $M$. In contrast to the case of $2 \times 2$ determinants, the $2 \times 2$ permanents define an ideal which is neither…

In this paper, we study the complexity of computing the determinant of a matrix over a non-commutative algebra. In particular, we ask the question, "over which algebras, is the determinant easier to compute than the permanent?" Towards…

An efficient continuous-time path-integral Quantum Monte Carlo algorithm for the lattice polaron is presented. It is based on Feynman's integration of phonons and subsequent simulation of the resulting single-particle self-interacting…

We define two new families of polynomials that generalize permanents and prove upper and lower bounds on their determinantal complexities comparable to the known bounds for permanents. One of these families is obtained by replacing…

We show that a formalism proposed by Creutz to evaluate Grassmann integrals provides an algorithm of complexity $O(2^n n^3)$ to compute the generating function for the sum of the permanental minors of a matrix of order $n$. This algorithm…

Jerrum, Sinclair and Vigoda (2004) showed that the permanent of any square matrix can be estimated in polynomial time. This computation can be viewed as approximating the partition function of edge-weighted matchings in a bipartite graph.…

We present an efficient algorithm for computing the permanent for matrices of size N that can written as a product of L block diagonal matrices with blocks of size at most 2. For fixed L, the time and space resources scale linearly in N,…