Related papers: A note about words which coincide except in one po…

This short note present a "proof" of $P\neq NP$. The "proof" with double quotation marks is to indicate that we do not know whether the proof is correct or not (We're confused because we do know in which we make the mistakes).

In this note we show that the only result of [Rocky Mountain J. Math. 54 (2024), no. 4, 995--1004] is nothing more than a misformulated version of an exercise from classical texts, presented with a flawed proof. To place the matter on…

The aim of this note is to show that Poincar\'e inequalities imply corresponding weighted versions in a quite general setting. Fractional Poincar\'e inequalities are considered, too. The proof is short and does not involve covering…

We give a brief survey of recent results on word maps on simple groups and polynomial maps on simple associative and Lie algebras. Our focus is on parallelism between these theories, allowing one to state many new open problems and giving…

We survey known results and open problems in abelian combinatorics on words. Abelian combinatorics on words is the extension to the commutative setting of the classical theory of combinatorics on words. The extension is based on…

The object of this short note is to prove a theorem and present a conjecture for the number of even entries in the character table of the symmetric group.

It is shown that operations of equivalence cannot serve for building algebras which would induce orthomodular lattices as the operations of implication can. Several properties of equivalence operations have been investigated. Distributivity…

The paper presents a counterexample to the Hodge conjecture.

In this short note, we will give the key point of the section conjecture of Grothendieck, that is reformulated by monodromy actions. Here, we will also give the result of the section conjecture for algebraic schemes over a number field.

A short, fairly self-contained proof is given of the Poincar\'e Conjecture. In the previous version there was an error on Page 8. This gap has now been filled.

The purpose of this note is to give a number of open problems on matching theory and their relation to the well-known results in this area. We also give a linear analogue of the acyclic matchings.

In this note we present a characterisation of all unary and binary patterns that do not only contain variables, but also reversals of their instances. These types of variables were studied recently in either more general or particular…

In this article, I introduce a group-theoretical method to prove positivity of certain linear combinations (with coefficients generally lying in $\mathbb{C}$) of exponential functions under a set of semidefinite linear constraints. The…

We study word maps with constants on symmetric groups. Even though there are mixed identities of bounded length that are valid for all symmetric groups, we show that no such identities hold in a metric sense. Moreover, we prove that word…

In a consistent text, many words and phrases are repeatedly used in more than one sentence. When an identical phrase (a set of consecutive words) is repeated in different sentences, the constituent words of those sentences tend to be…

The aim of this paper is to establish some metrical coincidence and common fixed point theorems with an arbitrary relation under an implicit contractive condition which is general enough to cover a multitude of well known contraction…

An interesting phenomenon in combinatorics on words is when every recurrent word satisfying some avoidance constraints has the same factor set as a morphic word. An early example is the Hall-Thue word, fixed point of the morphism…

This note provides a new approach to a result of Foregger and related earlier results by Keilson and Eberlein. Using quite different techniques, we prove a more general result from which the others follow easily. Finally, we argue that the…

This paper proposes a simple test for compositionality (i.e., literal usage) of a word or phrase in a context-specific way. The test is computationally simple, relying on no external resources and only uses a set of trained word vectors.…

We establish coupled fixed point theorems for contraction involving rational expressions in partially ordered metric spaces.