Related papers: Greedy Regular Convolutions
We consider the problem of enumeration of primitive TSRs of order n over any finite field. Here we prove the existence of primitive TSRs of order two over binary field extensions. Moreover we give a general search algorithm for primitive…
We collect various known results (about plane curves and the moduli space of stable maps) to derive new recursive formulas enumerating low genus plane curves of any degree with various behaviors. Recursive formulas are given for the…
The classic model of computable randomness considers martingales that take real or rational values. Recent work by Bienvenu et al. (2012) and Teutsch (2014) shows that fundamental features of the classic model change when the martingales…
Suppose that M is countable, binary, primitive, homogeneous, and simple, and hence 1-based. We prove that the SU-rank of the complete theory of M is~1. It follows that M is a random structure. The conclusion that M is a random structure…
A simple proof of the fact that each rank-one infinite measure preserving (i.m.p.) transformation is subsequence weakly rationally ergodic is found. Some classes of funny rank-one i.m.p. actions of Abelian groups are shown to be subsequence…
We derive new results for the performance of a simple greedy algorithm for finding large independent sets and matchings in constant degree regular graphs. We show that for $r$-regular graphs with $n$ nodes and girth at least $g$, the…
A base for a permutation group $G$ acting on a set $\Omega$ is a subset $\mathcal{B}$ of $\Omega$ whose pointwise stabiliser $G_{(\mathcal{B})}$ is trivial. There is a natural greedy algorithm for constructing a base of relatively small…
In [A. Frid, S. Puzynina, L.Q. Zamboni, \textit{On palindromic factorization of words}, Adv. in Appl. Math. 50 (2013), 737-748], it was conjectured that any infinite word whose palindromic lengths of factors are bounded is ultimately…
The main result of the present paper is bounded elementary generation of the Steinberg groups $\mathrm{St}(\Phi,R)$ for simply laced root systems $\Phi$ of rank $\ge 2$ and arbitrary Dedekind rings of arithmetic type. Also, we prove bounded…
We consider minimizing a smooth function subject to a summation constraint over its variables. By exploiting a connection between the greedy 2-coordinate update for this problem and equality-constrained steepest descent in the 1-norm, we…
Let k be an algebraically closed field of characteristic 0. Musson and vandenBergh classified primitive ideals for rings of torus invariant differential operators. This classification applies in particular to subquotients of localized…
In this paper, we carry out a fairly comprehensive study of special classes of numerical semigroups, and their tangent cones, generated by the sequence of partial sums of an arithmetic progression, in embedding dimension $5$. These classes…
A simple permutation is one that does not map a nontrivial interval onto an interval. It was recently proved by Albert and Atkinson that a permutation class with only finitely simple permutations has an algebraic generating function. We…
We prove that for infinite rank-one transformations satisfying a property called "partial boundedness," the only commuting transformations are powers of the original transformation. This shows that a large class of infinite…
We investigate numerical semigroups generated by any quadratic sequence with initial term zero and an infinite number of terms. We find an efficient algorithm for calculating the Ap\'ery set, as well as bounds on the elements of the Ap\'ery…
We survey general properties of multiplicative arithmetic functions of several variables and related convolutions, including the Dirichlet convolution and the unitary convolution. We introduce and investigate a new convolution, called gcd…
This paper focuses on greedy expansions, one possible representation of numbers, and on arithmetical operations with them. Performing addition or multiplication some additional digits can appear. We study bounds on the number of such digits…
In this paper we study some structure properties of primitive weird numbers in terms of their factorization. We give sufficient conditions to ensure that a positive integer is weird. Two algorithms for generating weird numbers having a…
We study the convolution of functions of the form \[ f_\alpha (z) := \dfrac{\left( \frac{1 + z}{1 - z} \right)^\alpha - 1}{2 \alpha}, \] which map the open unit disk of the complex plane onto polygons of 2 edges when $\alpha\in(0,1)$. We…
Given a positive rational number $n/d$ with $d$ odd, its odd greedy expansion starts with the largest odd denominator unit fraction at most $n/d$, adds the largest odd denominator unit fraction so the sum is at most $n/d$, and continues as…