Related papers: Counting words with Laguerre series

Inspired by the paper of Bonichon, Bousquet-M\'elou, Dorbec and Pennarun, we give a system of functional equations which characterise the ordinary generating function, $U(x),$ for the number of planar Eulerian orientations counted by edges.…

We say that a word $w$ on a totally ordered alphabet avoids the word $v$ if there are no subsequences in $w$ order-equivalent to $v$. In this paper we suggest a new approach to the enumeration of words on at most $k$ letters avoiding a…

A large set of signals can sometimes be described sparsely using a dictionary, that is, every element can be represented as a linear combination of few elements from the dictionary. Algorithms for various signal processing applications,…

We consider questions related to the structure of infinite words (over an integer alphabet) with bounded additive complexity, i.e., words with the property that the number of distinct sums exhibited by factors of the same length is bounded…

We develop combinatorial test generation algorithms for progressively more powerful theorem provers, covering formula languages ranging from the implicational fragment of intuitionistic logic to full intuitionistic propositional logic. Our…

This paper presents a novel approach to automatically solving arithmetic word problems. This is the first algorithmic approach that can handle arithmetic problems with multiple steps and operations, without depending on additional…

A method based on the quantum Calogero-Sutherland model is used to obtain generating functions for characters and multiplicities of $A_3$. Some comments on other rank three algebras are offered.

For a regular $2n$-gon there are $(2n-1)!!$ ways to match and glue the $2n$ sides. The Harer-Zagier bivariate generating function enumerates the gluings by $n$ and the genus $g$ of the attendant surface and leads to a recurrence equation…

Nowadays there are several classes of constrained codes intended for different applications. The following two large classes can be distinguished. The first class contains codes with local constraints; for example, the source data must be…

We exhibit combinatorial results on Christoffel words and binary balanced words that are motivated by their geometric interpretation as approximations of digital segments. We give a closed formula for counting the exact number of balanced…

In a paper entitled Binary lambda calculus and combinatory logic, John Tromp presents a simple way of encoding lambda calculus terms as binary sequences. In what follows, we study the numbers of binary strings of a given size that represent…

In the context of software testing, generating complex data inputs is frequently performed using a grammar-based specification. For combinatorial reasons, an exhaustive generation of the data -- of a given size -- is practically impossible,…

We present counting methods for some special classes of multivariate polynomials over a finite field, namely the reducible ones, the s-powerful ones (divisible by the s-th power of a nonconstant polynomial), and the relatively irreducible…

We use combinatorial and generating function techniques to enumerate various sets of involutions which avoid 231 or contain 231 exactly once. Interestingly, many of these enumerations can be given in terms of $k$-generalized Fibonacci…

We consider the distributions of the lengths of the longest weakly increasing and strongly decreasing subsequences in words of length N from an alphabet of k letters. We find Toeplitz determinant representations for the exponential…

In the first part of this survey, we present classical notions arising in combinatorics on words: growth function of a language, complexity function of an infinite word, pattern avoidance, periodicity and uniform recurrence. Our…

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…

A lower time bound $\Omega(\min(\nu(x), n-\nu(x))$ for counting the number of ones in a binary input word $x$ of length $n$ is presented, where $\nu(x)$ is the number of ones. The operations available are increment, decrement, bit-wise…

We generalize generating functions for hypergeometric orthogonal polynomials, namely Jacobi, Gegenbauer, Laguerre, and Wilson polynomials. These generalizations of generating functions are accomplished through series rearrangement using…

We give a formula for the bivariate generating function of a stationary 1-dependent counting process in terms of its run probability generating function, with a probabilistic proof. The formula reduces to the well known bivariate generating…