Related papers: Analytic aspects of the shuffle product
This is the first of two articles devoted to a comprehensive exposition of the generating-function method for computing fusion rules in affine Lie algebras. The present paper is entirely devoted to the study of the tensor-product…
We construct uncountably generated algebras inside the following sets of special functions: Sierpi\'nski-Zygmund functions, perfectly everywhere surjective functions and nowhere continuous Darboux functions. All conclusions obtained in this…
The literal and the initial literal shuffle have been introduced to model the behavior of two synchronized processes. However, it is not possible to describe the synchronization of multiple processes. Furthermore, both restricted forms of…
This paper is devoted to the presentation of combinatorial bialgebras whose coproduct is defined with the help of a commutative semigroup. We consider this setting in order to give a general framework which admits as special cases the…
Algebraic effects offer a versatile framework that covers a wide variety of effects. However, the family of operations that delimit scopes are not algebraic and are usually modelled as handlers, thus preventing them from being used freely…
We construct and study new generalisations to rooted trees and forests of some properties of shuffles of words. First, we build a coproduct on rooted trees which, together with their shuffle, endow them with bialgebra structure. We then…
We identify a subclass of the regular commutative languages that is closed under the iterated shuffle, or shuffle closure. In particular, it is regularity-preserving on this subclass. This subclass contains the commutative group languages…
In this paper, we investigate the shuffle product relations for Euler-Zagier multiple zeta functions as functional relations. To this end, we generalize the classical partial fraction decomposition formula and give two proofs. One is based…
The theory of operated algebras has played a pivotal role in mathematics and physics. In this paper, we introduce a $\lambda$-TD algebra that appropriately includes both the Rota-Baxter algebra and the TD-algebra. The explicit construction…
Circular splicing systems are a formal model of a generative mechanism of circular words, inspired by a recombinant behaviour of circular DNA. Some unanswered questions are related to the computational power of such systems, and finding a…
We propose a call-by-value lambda calculus extended with a new construct inspired by abductive inference and motivated by the programming idioms of machine learning. Although syntactically simple the abductive construct has a complex and…
Recently researchers working in the LFG framework have proposed algorithms for taking advantage of the implicit context-free components of a unification grammar [Maxwell 96]. This paper clarifies the mathematical foundations of these…
This paper introduces a robust class of functions from finite words to integers that we call Z-polyregular functions. We show that it admits natural characterizations in terms of logics, Z-rational expressions, Z-rational series and…
We enumerate the independent sets of several classes of regular and almost regular graphs and compute the corresponding generating functions. We also note the relations between these graphs and other combinatorial objects and, in some…
In the present paper we show that there are infinitely many classes of term functions in the free-void generated diagonalizable algebra, which are precomplete with respect to parametrical expressibility of functions.
Probabilistic context-free grammars have a long-term record of use as generative models in machine learning and symbolic regression. When used for symbolic regression, they generate algebraic expressions. We define the latter as equivalence…
We consider functions of natural numbers which allow a combinatorial interpretation as density functions (speed) of classes of relational structures, s uch as Fibonacci numbers, Bell numbers, Catalan numbers and the like. Many of these…
This is the first of two articles devoted to a exposition of the generating-function method for computing fusion rules in affine Lie algebras. The present paper is entirely devoted to the study of the tensor-product (infinite-level) limit…
Shuffle projection is motivated by the verification of safety properties of special parameterized systems. Basic definitions and properties, especially related to alphabetic homomorphisms, are presented. The relation between iterated…
In this manuscript, we investigate some properties of certain counting functions, associated to the ergodic sums computed along the periodic orbits of the skew-product map, related to a finitely generated rational semigroup. To be precise,…