DeepAI AI Chat
Log In Sign Up

Polyominoes and graphs built from Fibonacci words

11/10/2022
by   Sergey Kirgizov, et al.
Universidad Nacional de Colombia
Université de Bourgogne
0

We introduce the k-bonacci polyominoes, a new family of polyominoes associated with the binary words avoiding k consecutive 1's, also called generalized k-bonacci words. The polyominoes are very entrancing objects, considered in combinatorics and computer science. The study of polyominoes generates a rich source of combinatorial ideas. In this paper we study some properties of k-bonacci polyominoes. Specifically, we determine their recursive structure and, using this structure, we enumerate them according to their area, semiperimeter, and length of the corresponding words. We also introduce the k-bonacci graphs, then we obtain the generating functions for the total number of vertices and edges, the distribution of the degrees, and the total number of k-bonacci graphs that have a Hamiltonian cycle.

READ FULL TEXT

page 1

page 2

page 3

page 4

12/22/2019

Catalan words avoiding pairs of length three patterns

Catalan words are particular growth-restricted words counted by the epon...
07/29/2021

Mesosome Avoidance

We consider avoiding mesosomes – that is, words of the form xx' with x' ...
03/18/2018

Descent distribution on Catalan words avoiding a pattern of length at most three

Catalan words are particular growth-restricted words over the set of non...
02/01/2023

Distributed CONGEST Algorithm for Finding Hamiltonian Paths in Dirac Graphs and Generalizations

We study the problem of finding a Hamiltonian cycle under the promise th...
01/03/2022

Realizations of Rigid Graphs

A minimally rigid graph, also called Laman graph, models a planar framew...
10/01/2020

On the recursive structure of multigrid cycles

A new non-adaptive recursive scheme for multigrid algorithms is introduc...
06/25/2021

Asymptotic bit frequency in Fibonacci words

It is known that binary words containing no k consecutive 1s are enumera...