Related papers: Colored compositions, Invert operator and elegant …
In this paper, we study the composition operators on an algebra of Dirichlet series, the analogue of the Wiener algebra of absolutely convergent Taylor series, which we call the Wiener-Dirichlet algebra. We study the connection between the…
We give an explicit construction of the generating set of a colored operad that implements theta theory in the mathematical model of Minimalism in generative linguistics, in the form of a coloring algorithm for syntactic objects. We show…
The concept of graph compositions is related to several number theoretic concepts, including partitions of positive integers and the cardinality of the power set of finite sets. This paper examines graph compositions where the total number…
We use the combinatorial properties of central sets to prove a result about the existence of exponential monochromatic patterns, in the style of Hindman's Finite Sums Theorem. More precisely, we prove that for every finite coloring of the…
The Composite Operator Method (COM) is formulated, its internals illustrated in detail and some of its most successful applications reported. COM endorses the emergence, in strongly correlated systems (SCS), of composite operators,…
For a given integer $d\ge 1$, we consider $\binom{n+d-1}{d}$-color compositions of a positive integer $\nu$ for which each part of size $n$ admits $\binom{n+d-1}{d}$ colors. We give explicit formulas for the enumeration of such…
Integer compositions, integer partitions, Fibonacci numbers, and generalizations of these have recently been shown to be interconnected via two-toned tilings of horizontal grids. In this article, we present refinements of two-toned tilings,…
Colored operads were introduced in the 1970's for the purpose of studying homotopy invariant algebraic structures on topological spaces. In this paper we introduce colored operads in motivic stable homotopy theory. Our main motivation is to…
With the aim of completing the previous study by A. Or{\l}owski and the author concerning intertwining maps between induced representations and conjugation representation, termed here weighted class operators, we compute the latter…
We study the convergence of a family of numerical integration methods where the numerical integral is formulated as a finite matrix approximation to a multiplication operator. For bounded functions, the convergence has already been…
Color theme or color palette can deeply influence the quality and the feeling of a photograph or a graphical design. Although color palettes may come from different sources such as online crowd-sourcing, photographs and graphical designs,…
This paper studies the proof of Collatz conjecture for some set of sequence of odd numbers with infinite number of elements. These set generalized to the set which contains all positive odd integers. This extension assumed to be the proof…
We provide general conditions under which the algebras for a coloured operad in a monoidal model category carry a Quillen model structure, and prove a Comparison Theorem to the effect that a weak equivalence between suitable such operads…
In this thesis, we investigate the computational content and the logical strength of Ramsey's theorem and its consequences. For this, we use the frameworks of reverse mathematics and of computable reducibility. We proceed to a systematic…
In this article we tackle the combinatorics of coloured hard-dimer objects. This is achieved by identifying coloured hard-dimer configurations with a certain class of rooted trees that allow for an algebraic treatment in terms of…
For $a,b\in\mathbb{N}_0$, we consider $(an+b)$-color compositions of a positive integer $\nu$ for which each part of size $n$ admits $an+b$ colors. We study these compositions from the enumerative point of view and give a formula for the…
We investigate the usage of rule dependency graphs and their colorings for characterizing and computing answer sets of logic programs. This approach provides us with insights into the interplay between rules when inducing answer sets. We…
By studying Cameron's operator in terms of determinants, two kinds of "integer" sequences of incomplete numbers were introduced. One was the sequence of restricted numbers, including $s$-step Fibonacci sequences. Another was the sequence of…
There are many variations on partition functions for graph homomorphisms or colorings. The case considered here is a counting or hard constraint problem in which the range or color graph carries a free and vertex transitive Abelian group…
For $k\ge 1$, we consider interleaved $k$-tuple colorings of the nodes of a graph, that is, assignments of $k$ distinct natural numbers to each node in such a way that nodes that are connected by an edge receive numbers that are strictly…