Related papers: Rapid growth sequences
Given two quivers, each with a reddening sequence, we show how to construct a plethora of mutation cycles. We give several examples, including a generalization of the construction of long mutation cycles in earlier work by the second…
Modification of the particles in the course of the source evolution is considered. Influence of this effect on multiplicities and correlations of the particles is displayed, including an enhancement of the production rates and identical…
Sequential transitions between metastable states are ubiquitously observed in the neural system and underlie various cognitive functions. Although a number of studies with asymmetric Hebbian connectivity have investigated how such sequences…
This article is a sequel to a recent article by Eric Rowland and Reem Yassawi, presenting yet another approach to the fast determination of congruence properties of `famous' combinatorial sequences. The present approach can be taught to a…
Morphic sequences form a natural class of infinite sequences, typically defined as the coding of a fixed point of a morphism. Different morphisms and codings may yield the same morphic sequence. This paper investigates how to prove that two…
The basic object we consider is a certain model of continuum random tree, called the stable tree. We construct a fragmentation process $(F^-(t), t>=0)$ out of this tree by removing the vertices located under height $t$. Thanks to a…
We produce a long exact sequence whose terms are unit groups of associative algebras that behave as inner automorphisms of a given tensor. Our sequence generalizes known sequences for associative and non-associative algebras. In a manner…
Different ways to describe a permutation, as a sequence of integers, or a product of Coxeter generators, or a tree, give different choices to define a simple permutation. We recollect few of them, define new types of simple permutations,…
We describe a simple method that produces automatically closed forms for the coefficients of continued fractions expansions of a large number of special functions. The function is specified by a non-linear differential equation and initial…
In this research article, we consider the uniqueness sequences for multidimensional vector-valued Laplace transform. We establish the fundamental relationships between uniqueness sequences for one-dimensional Laplace transform and…
It is well known that every finite simple group can be generated by two elements and this leads to a wide range of problems that have been the focus of intensive research in recent years. In this survey article we discuss some of the…
Making use of a simplified model for protein folding, it can be shown that conformations which are particularly stable when their energy is minimized with respect to amino acid sequence (in the sense that they display a large energy gap to…
We recast homogeneous linear recurrence sequences with fixed coefficients in terms of partial Bell polynomials, and use their properties to obtain various combinatorial identities and multifold convolution formulas. Our approach relies on a…
A self-similar growth-fragmentation describes the evolution of particles that grow and split as time passes. Its genealogy yields a self-similar continuum tree endowed with an intrinsic measure. Extending results of Haas for pure…
We introduce several new constructions of finite posets with the number of linear extensions given by generalized continued fractions. We apply our results to the problem of the minimum number of elements needed for a poset with a given…
We prove almost sure convergence of the maximum degree in an evolving graph model combining a growing number of local choices with sublinear preferential attachment. At each step in the growth of the graph, a new vertex is introduced. Then…
Many growing networks possess accelerating statistics where the number of links added with each new node is an increasing function of network size so the total number of links increases faster than linearly with network size. In particular,…
This paper focuses on computing the frequency response and transfer functions for large self-similar networks under different circumstances. Modeling large scale systems is difficult due, typically, to the dimension of the problem, and…
We study classes of graded structures satisfying the properties of amalgamation, joint embedding and hereditariness. Given appropriate conditions, we can build a graded analogue of the Fraisse limit. Some examples such as the class of all…
This note presents an approach to studying the iterates of a mapping whose restriction to the complement of a finite set is continuous and open. The main examples to which the approach can be applied are piecewise monotone mappings defined…