Related papers: Fibonacci colored compositions and applications
A topological space is introduced in this paper. Just liking the plane, it's continuous, however its $n+1$ regions couldn't be mutually adjacent. Some important phenomenon about its cross-section are discussed. The geometric generating…
We introduce bud generating systems, which are used for combinatorial generation. They specify sets of various kinds of combinatorial objects, called languages. They can emulate context-free grammars, regular tree grammars, and synchronous…
This paper aims to undertake an exploration of the behavior of the moduli space of line arrangements while establishing its combinatorial interplay with the incidence structure of the arrangement. In the first part, we investigate…
We survey structures endowed with natural partial orderings and prove their universality. These partial orders include partial orders on sets of words, partial orders formed by geometric objects, grammars, polynomials and homomorphism order…
A modular or distributive lattice is `diamond-colored' if its order diagram edges are colored in such a way that, within any diamond of edges, parallel edges have the same color. Such lattices arise naturally in combinatorial representation…
Boolean combinations allow combining given combinatorial objects to obtain new, potentially more complicated, objects. In this paper, we initiate a systematic study of this idea applied to graphs. In order to understand expressive power and…
Let $(F_n)_{n\ge 1}$ be the Fibonacci sequence. Define $P(F_n): = (\sum_{i=1}^n F_i)_{n\ge 1}$; that is, the function $P$ gives the sequence of partial sums of $(F_n)$. In this paper, we first give an identity involving $P^k(F_n)$, which is…
In this paper we consider particular generalized compositions of a natural number with a given number of parts. Its number is a weighted polynomial coefficient. The number of all generalized compositions of a natural number is a weighted…
We explore a general method based on trees of elementary submodels in order to present highly simplified proofs to numerous results in infinite combinatorics. While countable elementary submodels have been employed in such settings already,…
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…
Sudoku grids can be thought of as graphs where the vertices are the squares of the grid, and edges join vertices in the same row, column, or sub-grid. A Sudoku puzzle corresponds to a partial proper coloring of the Sudoku graph. We provide…
In this paper we introduce a family of partitions of the set of natural numbers, Fibonacci-like partitions. In particular, we introduce a Fibonacci-like partition in a number of parts corresponding to the Fibonacci numbers, the standard…
This paper explores the Fibonacci sequence and the Golden Ratio as organizing principles for visual composition and abstraction in painting. The author shows how recursive proportional systems, long associated with natural growth and…
A proper $q$-coloring of a graph is an assignment of one of $q$ colors to each vertex of the graph so that adjacent vertices are colored differently. Sample uniformly among all proper $q$-colorings of a large discrete cube in the integer…
In his recent work, Andrews revisited two-color partitions with certain restrictions on the differences between consecutive parts, and he established three theorems linking these two-color partitions with more familiar kinds of partitions.…
We investigate compositions of a positive integer with a fixed number of parts, when there are several types of each natural number. These compositions produce new relationships among binomial coefficients, Catalan numbers, and numbers of…
This work is a study of polynomial compositions having a fixed number of terms. We outline a recursive method to describe these characterizations, give some particular results and discuss the general case. In the final sections, some…
The paper explores combinatorial properties of Fibonacci words and their generalizations within the framework of combinatorics on words. These infinite sequences, measures the diversity of subwords in Fibonacci words, showing non-decreasing…
The number of ways to tile an $n$-board (an $n\times1$ rectangular board) with $(\frac12,\frac12;1)$-, $(\frac12,\frac12;2)$-, and $(\frac12,\frac12;3)$-combs is $T_{n+2}^2$ where $T_n$ is the $n$th tribonacci number. A…
In this paper we would like to introduce some new methods for studying magic type-colorings of graphs or domination of graphs, based on combinatorial spectrum on polynomial rings. We hope that this concept will be potentially useful for the…