Related papers: Enumeration of Vuza Canons

Canonical Variate Analysis (CVA) is a multivariate statistical technique and a direct application of Linear Discriminant Analysis (LDA) that aims to find linear combinations of variables that best differentiate between groups in a dataset.…

This is a leisurely introductory account addressed to non-experts and based on previous work by the authors, on how methods borrowed from physics can be used to "count" an infinite number of points. We begin with the classical case of…

We define a notion of grading of a monoid T in a monoidal category C, relative to a class of morphisms M (which provide a notion of M-subobject). We show that, under reasonable conditions (including that M forms a factorization system),…

The classical Hurwitz numbers count the fixed-length transitive transposition factorizations of a permutation, with a remarkable product formula for the case of minimum length (genus $0$). We study the analogue of these numbers for…

Canonical Correlation Analysis (CCA) is a widely used statistical tool with both well established theory and favorable performance for a wide range of machine learning problems. However, computing CCA for huge datasets can be very slow…

The novelty of this paper is to construct the explicit combinatorial formula for the number of all distinct fuzzy matrices of finite order, which leads us to invent a new sequence. In order to achieve this new sequence, we analyze the…

The prime-counting function $\pi(x)$ which returns the number of primes smaller or equal to a given number is a topic of interest in number theory. An algorithm based on a cyclic group isomorphic to $Z/nZ$, the so-called $Z$-functions, was…

The CUR decomposition is a factorization of a low-rank matrix obtained by selecting certain column and row submatrices of it. We perform a thorough investigation of what happens to such decompositions in the presence of noise. Since CUR…

The traditional method of teaching canonical transformations involves the introduction of generating functions of various types. This method obscures the underlying structure of the Hamiltonian least-action principle, and can make a…

In this work we look at the original fractional calculus of variations problem in a somewhat different way. As a simple consequence, we show that a fractional generalization of a classical problem has a solution without any restrictions on…

We describe a method to compute renormalized coupling constants in a Monte Carlo renormalization group calculation. It can be used, e.g., for lattice spin or gauge models. The basic idea is to simulate a joint system of block spins and…

We show that the unitary factor U in the polar decomposition of a nonsingular matrix Z = U H is the minimizer for both ||Log(Q^* Z)|| and ||sym (Log(Q^*Z))|| over unitary Q, for any given invertible complex n-times-n matrix Z, for any…

We consider a cyclic analogue of multiple zeta values (CMZVs), which has two kinds of expressions; series and integral expression. We prove an `integral$=$series' type identity for CMZVs. By using this identity, we construct two classes of…

Let $G$ be a finite cyclic group, written additively, and let $A,\ B$ be nonempty subsets of $G$. We will say that $G= A+B$ is a \textit{factorization} if for each $g$ in $G$ there are unique elements $a,\ b$ of $G$ such that $g=a+b, \ a\in…

Assuming 0^sharp does not exist, kappa is an uncountable cardinal and for all cardinals lambda with kappa <= lambda < kappa^{+ omega}, 2^lambda = lambda^+, we present a ``mini-coding'' between kappa and kappa^{+ omega}. This allows us to…

This contains a new version of the so-called non-commutative Gauss algorithm for polycyclic groups. Its results allow to read off the order and the index of a subgroup in an (possibly infinite) polycyclic group.

In 2017, Michael Cuntz gave a definition of reducibility of quiddity cycles of frieze patterns: It is reducible if it can be written as a sum of two other quiddity cycles. We discuss the commutativity and associativity of this sum operator…

Canon permutations are permutations of the multiset having $k$ copies of each integer between $1$ and $n$, with the property that the subsequences obtained by taking the $j$th copy of each entry, for each fixed $j$, are all the same. For…

In this paper we describe new noncommutative factorizations of functions related to $d$-th tensor powers of Carlitz's $\mathbb F_q[\theta]$-module for $d\geq 1$, called higher sine functions. In recent work by the second author,…

It is well known that the Lorenz system has $Z_2$-symmetry. Using introducted in math.DS/0105147 topological covering-coloring a new representation for the Lorenz system is obtained. Deleting coloring leads to the factorized Lorenz system…