Related papers: Some Combinatorial Operators in Language Theory
An operad describes a category of algebras and a (co)homology theory for these algebras may be formulated using the homological algebra of operads. A morphism of operads $f:\mathcal{O}\rightarrow\mathcal{P}$ describes a functor allowing a…
This paper introduces the concept of Bessel multipliers. These operators are defined by a fixed multiplication pattern, which is inserted between the Analysis and synthesis operators. The proposed concept unifies the approach used for Gabor…
We survey general properties of multiplicative arithmetic functions of several variables and related convolutions, including the Dirichlet convolution and the unitary convolution. We introduce and investigate a new convolution, called gcd…
We introduce certain raising and lowering operators for Macdonald polynomials (of type $A_{n-1}$) by means of Dunkl operators. The raising operators we discuss are a natural $q$-analogue of raising operators for Jack polynomials introduced…
We develop an operator algebraic framework for generalized Cardano polynomials and show how their structure naturally leads to an operator formulation of Cardano method that is compatible with tools and concepts from quantum information…
This thesis proposes a combinatorial generalization of a nilpotent operator on a vector space. The resulting object is highly natural, with basic connections to a variety of fields in pure mathematics, engineering, and the sciences. For the…
This paper grew out of the author's work on arXiv:2504.18460. Differential operators in the sense of Grothendieck acting between modules over a commutative ring can be interpreted as torsion elements in the bimodule of all operators with…
The new notion of operator/matrix $k$-tone functions is introduced, which is a higher order extension of operator/matrix monotone and convex functions. Differential properties of matrix $k$-tone functions are shown. Characterizations,…
In a very recent work, G. E. Andrews defined the combinatorial objects which he called {\it singular overpartitions} with the goal of presenting a general theorem for overpartitions which is analogous to theorems of Rogers--Ramanujan type…
Polynomials in a category have been studied as a generalization of the traditional notion in mathematics. Their construction has recently been extended to higher groupoids, as formalized in homotopy type theory, by Finster, Mimram, Lucas…
We provide a survey of the current state of the study of diagonals of operators, especially selfadjoint operators. In addition, we provide a few new results made possible by recent work of M\"uller-Tomilov and Kaftal-Loreaux. This is an…
We introduce multilinear analogues of dyadic paraproduct operators and Haar Multipliers, and study boundedness properties of these operators and their commutators. We also characterize dyadic BMO functions via the boundedness of certain…
This paper investigates summability principles for multilinear summing operators. The main result presents a novel inclusion theorem for a class of summing operators, which generalizes several classical results. As applications, we derive…
In this article, we introduce the notion of cycling operations of arbitrary order in Garside groups, which is a full generalization of the cycling and decycling operations. Theoretically, this notion together with other related concepts…
Motivated by an ongoing project on computer aided derivation of asymptotic models governed by partial differential equations, we introduce a class of term transformations that consists of traversal strategies and insertion of contexts. We…
Around 20 years ago, M. Van den Bergh introduced double Poisson brackets as operations on associative algebras inducing Poisson brackets under the representation functor. Weaker versions of these operations, called modified double Poisson…
Computational effects are commonly modelled by monads, but often a monad can be presented by an algebraic theory of operations and equations. This talk is about monads and algebraic theories for languages for inference, and their…
We unify parastatistics, defined as triple operator algebras represented on Fock space, in a simple way using the transition number operators. We express them as a normal ordered expansion of creation and annihilation operators. We discuss…
We exhaustively investigate possible combinations of a boolean operation together with a catenation. In many cases we prove and improve some conjectures by Brzozowski. For each family of operation, we endeavour to provide a common witness…
In this paper we introduce an abstract approach to the notion of absolutely summing multilinear operators. We show that several previous results on different contexts (absolutely summing, almost summing, Cohen summing) are particular cases…