Related papers: Fixed hooks in arbitrary columns
In this paper we consider the sequence whose n^{th} term is the number of h-vectors of length n. We show that the n^{th} term of this sequence is bounded above by the n^{th} Fibonacci number and bounded below by the number if integer…
In this article we studied the relationship between metric spaces and multiplicative metric spaces. Also, we pointed out some fixed and common fixed point results under some contractive conditions in multiplicative metric spaces can be…
Michael Handel proved in Handel (1999) the existence of a fixed point for an orientation preserving homeomorphism of the open unit disk that can be extended to the closed disk, provided that it has points whose orbits form an oriented cycle…
We consider bounded 2-metric spaces satisfying an additional axiom, and show that a contractive mapping has either a fixed point or a fixed line.
In this paper, our aim is to obtain new fixed-disc results on metric spaces. To do this, we present a new approach using the set of simulation functions and some known fixed-point techniques. We do not need to have some strong conditions…
Persistent homology is a popular and useful tool for analysing finite metric spaces, revealing features that can be used to distinguish sets of unlabeled points and as input into machine learning pipelines. The famous stability theorem of…
In some particular cases we give criteria for morphic sequences to be almost periodic (=uniformly recurrent). Namely, we deal with fixed points of non-erasing morphisms and with automatic sequences. In both cases a polynomial-time algorithm…
We consider colored compositions where only some parts are allowed different colors, depending on their locations in the composition. The counting sequences are obtained through generating functions. Connections to many other combinatorial…
Let $b_{n,k}$ denote the number of hooks of length $k$ in all the $t$-regular partitions of $n$. Singh and Barman raised the question of finding the relation between $b_{t,2}(n)$ and $b_{t,1}(n)$. Kim showed that there exists $N$ such that…
Understanding the Impossibility of a Tie in Hex via Fixed Point Theorems, the Hex Theorem, and Their Equivalence.
In this paper, we prove several fixed point theorems on both of normal partially ordered Banach spaces and regular partially ordered Banach spaces by using the normality, regularity, full regularity, and chain -complete property. Then, by…
Nonexpansive mappings play a central role in modern optimization and monotone operator theory because their fixed points can describe solutions to optimization or critical point problems. It is known that when the mappings are sufficiently…
A topological space has the fixed point property if every continuous self-map of that space has at least one fixed point. We demonstrate that there are serious restraints imposed by the requirement that there be a choice of fixed points…
This paper discusses a general and useful stability principle which, roughly speaking, says that given a uniformly continuous function defined on an arbitrary metric space, if the function is bounded on the constraint set and we slightly…
Recently, Griffin, Ono, and Tsai examined the distribution of the number of $t$-hooks in partitions of $n$, which was later followed by the work of Craig, Ono, and Singh on the distribution of the number of $t$-hooks in self-conjugate…
Graded posets frequently arise throughout combinatorics, where it is natural to try to count the number of elements of a fixed rank. These counting problems are often $\#\textbf{P}$-complete, so we consider approximation algorithms for…
Some results on fixed points related to the contractive compositions of bounded operators in complete metric spaces are discussed through the manuscript. The class of composite operators under study can include, in particular, sequences of…
In the paper, the authors present several new relations and applications for the combinatorial sequence that counts the possible partitions of a finite set with the restriction that the size of each block is contained in a given set. One of…
We define, for an arbitrary partially ordered set, a multi-variable polynomial generalizing the hook polynomial.
Given an infinite word, enumerating its factors is an important exercise for understanding the structure of the word. The process of finding all the factors is quite tricky for two-dimensional words. In this paper, two possible ways of…