Related papers: Analytic aspects of the shuffle product
Our goal in this work is to found a closed form for rational generat- ing functions, these generate a various families of polynomials and generalized polynomials, in order to get the general recursive formula satisfied by these polynomials.
We consider paths in the plane with $(1,0),$ $(0,1),$ and $(a,b)$-steps that start at the origin, end at height $n,$ and stay to the left of a given non-decreasing right boundary. We show that if the boundary is periodic and has slope at…
Classes of algebraic structures that are defined by equational laws are called varieties or equational classes. A variety is finitely generated if it is defined by the laws that hold in some fixed finite algebra. We show that every…
A quantitative model of concurrent interaction is introduced. The basic objects are linear combinations of partial order relations, acted upon by a group of permutations that represents potential non-determinism in synchronisation. This…
The filtered derived category of an abelian category has played a useful role in subjects including geometric representation theory, mixed Hodge modules, and the theory of motives. We develop a natural generalization using current methods…
Indexed languages are a classical notion in formal language theory, which has attracted attention in recent decades due to its role in higher-order model checking: They are precisely the languages accepted by order-2 pushdown automata. The…
A new family of categorial grammars is proposed, defined by enriching basic categorial grammars with a conjunction operation. It is proved that the formalism obtained in this way has the same expressive power as conjunctive grammars, that…
In this paper, we define finitely additive, probability and modular functions over semiring-like structures. We investigate finitely additive functions with the help of complemented elements of a semiring. We also generalize some classical…
We consider the problem of learning the semantics of composite algebraic expressions from examples. The outcome is a versatile framework for studying learning tasks that can be put into the following abstract form: The input is a partial…
In order to study the analytic properties of the Goldbach generating function we consider a smooth version, similar to the Chebyshev function for the Prime Number Theorem. In this paper, we obtain explicit numerical estimates for the…
A permutation is said to be a square if it can be obtained by shuffling two order-isomorphic patterns. The definition is intended to be the natural counterpart to the ordinary shuffle of words and languages. In this paper, we tackle the…
We propose generative models for three types of extra-grammatical word formation phenomena abounding in English slang: Blends, Clippings, and Reduplicatives. Adopting a data-driven approach coupled with linguistic knowledge, we propose…
We present an example of a quadratic algebra given by three generators and three relations, which is automaton (the set of normal words forms a regular language) and such that its ideal of relations does not possess a finite Gr\"obner basis…
A combinatorial study discloses two surjective morphisms between generalized shuffle algebras and algebras generated by the colored Hurwitz polyz\^etas. The combinatorial aspects of the products and co-products involved in these algebras…
A longstanding question in cognitive science concerns the learning mechanisms underlying compositionality in human cognition. Humans can infer the structured relationships (e.g., grammatical rules) implicit in their sensory observations…
The role of coalgebras as well as algebraic groups in non-commutative probability has long been advocated by the school of von Waldenfels and Sch\"urmann. Another algebraic approach was introduced more recently, based on shuffle and pre-Lie…
The method of direct computation of universal (fibred) product in the category of commutative associative algebras of finite type with unity over a field is given and proven. The field of coefficients is not supposed to be algebraically…
An algebra is finitely related (or has finite degree) if its term functions are determined by some finite set of finitary relations. Nilpotent monoids built from words, via Rees quotients of free monoids, have been used to exhibit many…
Some new connections are given between linear orderings and triangular operator algebras. A lexicograhic product is defined for triangular operator algebras and the Jacobson radical of an infinite lexicographic product of upper triangular…
In this technical report, certain interesting classification of arithmetical functions is proposed. The notion of additively decomposable and multiplicatively decomposable arithmetical functions is proposed. The concepts of arithmetical…