Related papers: Commutation matrices and Commutation tensors
We study a natural q-analogue of a class of matrices with noncommutative entries, which were first considered by Yu. I. Manin in 1988 in relation with quantum group theory, (called Manin Matrices in [5]) . These matrices we shall call…
In this note, we discuss the shift retrieval problems, both classical and compressed, and provide connections between them using circulant matrices. We review the properties of circulant matrices necessary for our calculations and then show…
In 1989 we proposed to employ Vandermonde and Hankel multipliers to transform into each other the matrix structures of Toeplitz, Hankel, Vandermonde and Cauchy types as a means of extending any successful algorithm for the inversion of…
We solve tensor balancing, rescaling an Nth order nonnegative tensor by multiplying N tensors of order N - 1 so that every fiber sums to one. This generalizes a fundamental process of matrix balancing used to compare matrices in a wide…
Tensor train (TT) decomposition is a powerful representation for high-order tensors, which has been successfully applied to various machine learning tasks in recent years. However, since the tensor product is not commutative, permutation of…
In this text we review a few structural properties of matrix models that should at least partly generalize to random tensor models. We review some aspects of the loop equations for matrix models and their algebraic counterpart for tensor…
We propose a new method to enumerate alternating knots using a transfer matrix approach. We apply it to count numerically various objects, including prime alternating tangles with two connected components, up to order 18--22, and comment on…
A brief presentation of basic definitions and notation used in permutation patterns research.
Discriminating data classes emanating from sensors is an important problem with many applications in science and technology. We describe a new transform for pattern identification that interprets patterns as probability density functions,…
We introduce a new class of permutations, called web permutations. Using these permutations, we provide a combinatorial interpretation for entries of the transition matrix between the Specht and web bases, which answers Rhoades's question.…
Truncated Fourier Transforms (TFTs), first introduced by Van der Hoeven, refer to a family of algorithms that attempt to smooth "jumps" in complexity exhibited by FFT algorithms. We present an in-place TFT whose time complexity, measured in…
In the following short paper we list some useful results concerning determinants and inverses of matrices. First we show, how to calculate determinants of $d \times d$ matrices, if their traces are known. As a next step $4 \times 4$…
In this paper, a matrix is said to be prime if the row and column of this matrix are both prime numbers. We establish various necessary and sufficient conditions for developing matrices into the sum of tensor products of prime matrices. For…
We discuss permutation representations which are obtained by the natural action of $S_n \times S_n$ on some special sets of invertible matrices, defined by simple combinatorial attributes. We decompose these representations into…
Beginning with work of Zeilberger on classical pattern counts, there are a variety of structural results for moments of permutation statistics applied to random permutations. Using tools from representation theory, Gaetz and Ryba…
We prove conjectures of the third author [L. Tevlin, Proc. FPSAC'07, Tianjin] on two new bases of noncommutative symmetric functions: the transition matrices from the ribbon basis have nonnegative integral coefficients. This is done by…
We describe a new method for finding patterns in permutations that produce a given pattern after the permutation has been passed once through a stack. We use this method to describe West-3-stack-sortable permutations, that is, permutations…
This paper presents a study of the properties of a matrix model that was introduced to describe transitions between all Wigner surmises of Random Matrix theory. New results include closed-form exact analytical expressions for the…
We present a new algorithm for fast matrix multiplication using tensor decompositions which have special features. Thanks to these features we obtain exponents lower than what the rank of the tensor decomposition suggests. In particular for…
We study matrix identities involving multiplication and unary operations such as transposition or Moore-Penrose inversion. We prove that in many cases such identities admit no finite basis.