Related papers: Prolific Compositions
An interval in a combinatorial structure S is a set I of points which relate to every point from S I in the same way. A structure is simple if it has no proper intervals. Every combinatorial structure can be expressed as an inflation of a…
The Collatz map is defined for a positive even integer as half that integer, and for a positive odd integer as that integer threefold, plus one. The Collatz conjecture states that when the map is iterated the number one is eventually…
In this paper, we study the structure of the set of tilings produced by any given tile-set. For better understanding this structure, we address the set of finite patterns that each tiling contains. This set of patterns can be analyzed in…
This work is a study of polynomial compositions having a fixed number of terms. We outline a recursive method to describe these characterizations, give some particular results and discuss the general case. In the final sections, some…
An infinite permutation is a linear order on the set N. We study the properties of infinite permutations generated by fixed points of some uniform binary morphisms, and find the formula for their complexity.
In this note, we consider ordered partitions of integers such that each entry is no more than a fixed portion of the sum. We give a method for constructing all such compositions as well as both an explicit formula and a generating function…
An integer composition of a nonnegative integer $n$ is a tuple $(\pi_1,\ldots,\pi_k)$ of nonnegative integers whose sum is $n$; the $\pi_i$'s are called the parts of the composition. For fixed number $k$ of parts, the number of $f$-weighted…
Factorization models express a statistical object of interest in terms of a collection of simpler objects. For example, a matrix or tensor can be expressed as a sum of rank-one components. However, in practice, it can be challenging to…
A composition of $n\in\NN$ is an ordered collection of one or more positive integers whose sum is $n$. The number of summands is called the number of parts of the composition. A palindromic composition of $n$ is a composition of $n$ in…
We determine all composition-closed equational classes of Boolean functions. These classes provide a natural generalization of clones and iterative algebras: they are closed under composition, permutation and identification…
This dissertation presents a multifaceted look into the structural decomposition of permutation classes. The theory of permutation patterns is a rich and varied field, and is a prime example of how an accessible and intuitive definition…
We introduce and consider a certain probability question involving elementary number theory and the likelihood that a fixed prime will appear in a certain recursively defined factorization of an integer. We derive several convergent…
Graph compositions generalize both integer compositions and partitions of a finite set. We develop formulas, generating functions and recurrence relations for composition counting functions for several families of graphs.
We introduce the notion of multi-pattern, a combinatorial abstraction of polyphonic musical phrases. The interest of this approach lies in the fact that this offers a way to compose two multi-patterns in order to produce a longer one. This…
Interestingness is an important criterion by which we judge knowledge discovery. But, interestingness has escaped all attempts to capture its intuitive meaning into a concise and comprehensive form. A unifying paradigm is formulated by…
We use a probabilistic method to produce some combinatorial inequalities by considering pattern containment in permutations and words.
Many random combinatorial objects have a component structure whose joint distribution is equal to that of a process of mutually independent random variables, conditioned on the value of a weighted sum of the variables. It is interesting to…
We find generating functions the number of strings (words) containing a specified number of occurrences of certain types of order-isomorphic classes of substrings called subword patterns. In particular, we find generating functions for the…
We define the operation of composing two hereditary classes of permutations using the standard composition of permutations as functions and we explore properties and structure of permutation classes considering this operation. We mostly…
A \Def{composition} of a positive integer $n$ is a $k$-tuple $(\l_1, \l_2, \dots, \l_k) \in \Z_{> 0}^k$ such that $n = \l_1 + \l_2 + \dots + \l_k$. Our goal is to enumerate those compositions whose parts $\l_1, \l_2, \dots, \l_k$ avoid a…