Related papers: On Restricted Ternary Words and Insets
We study the connections between three seemingly different combinatorial structures - "uniform" brackets in statistics and probability theory, "containers" in online and distributed learning theory, and "combinatorial Macbeath regions", or…
In this paper, we explore applications of combinatorics on words across various domains, including data compression, error detection, cryptographic protocols, and pseudorandom number generation. The examination of the theoretical…
We develop the technique of reduced word manipulation to give a range of results concerning reduced words and permutations more generally. We prove a broad connection between pattern containment and reduced words, which specializes to our…
A solution is proposed for the problem of composition of ordinary generating functions. A new class of functions that provides a composition of ordinary generating functions is introduced; main theorems are presented; compositae are written…
Using generating functions, we derive many identities involving balancing and Lucas-balancing polynomials. By relating these polynomials to Chebyshev polynomials of the first and second kind, and Fibonacci and Lucas numbers, we offer some…
We define and study the combinatorial properties of compositional Bernoulli numbers and polynomials within the framework of rational combinatorics.
We develop a method for counting words subject to various restrictions by finding a combinatorial interpretation for a product of weighted sums of Laguerre polynomials with parameter \alpha = -1. We describe how such a series can be…
Combinatorial $t$-designs have been an interesting topic in combinatorics for decades. It was recently reported that the image sets of a fixed size of certain special polynomials may constitute a $t$-design. Till now only a small amount of…
This paper proposes an extension to classical regular expressions by the addition of two operators allowing the inclusion of boolean formulae from the zeroth order logic. These expressions are called constrained expressions. The associated…
We investigate sumset decompositions of quite general sets with restricted prime factors. We manage to handle certain sets, such as the smooth numbers, even though they have little sieve amenability, and conclude that these sets cannot be…
In previous papers, for an arithmetical function $f_0$, we defined functions $f_m$ and $c_m$ and designated numbers of restricted words over a finite alphabet counted by these functions. In this paper, we examine the reverse problem for…
We study generating functions for the number of permutations on n letters avoiding 132 and an arbitrary permutation $\tau$ on k letters, or containing $\tau$ exactly once. In several interesting cases the generating function depends only on…
The main object of the paper is to reveal connections between Chebyshev polynomials of the first and second kinds and Fibonacci polynomials introduced by Catalan. This is achieved by relating the respective (ordinary and exponential)…
According to the distributional inclusion hypothesis, entailment between words can be measured via the feature inclusions of their distributional vectors. In recent work, we showed how this hypothesis can be extended from words to phrases…
This paper reviews some results regarding symbolic dynamics, correspondence between languages of dynamical systems and combinatorics. Sturmian sequences provide a pattern for investigation of one-dimensional systems, in particular interval…
This paper presents some finite combinatorics of set systems with applications to model theory, particularly the study of dependent theories. There are two main results. First, we give a way of producing lower bounds on VC_ind-density, and…
In this article, the 2-iterated Sheffer polynomials are introduced by means of generating function and operational representation. Using the theory of Riordan arrays and relations between the Sheffer sequences and Riordan arrays, a…
We count permutations avoiding a nonconsecutive instance of a two- or three-letter pattern, that is, the pattern may occur but only as consecutive entries in the permutation. Two-letter patterns give rise to the Fibonacci numbers. The…
We study some properties of restricted and associated Fubini numbers. In particular, they have the natural extensions of the original Fubini numbers in the sense of determinants. We also introduce modified Bernoulli and Cauchy numbers and…
Some of the classical orthogonal polynomials such as Hermite, Laguerre, Charlier, etc. have been shown to be the generating polynomials for certain combinatorial objects. These combinatorial interpretations are used to prove new identities…