Related papers: Sudo-Lyndon
Using algebraic transformations and equivalent reformulations we derive a number of new results from some earlier ones (by the author) in more accepted terms closely related to well-known conjectures of Bondy and Jung including a number of…
In this note we show that the known relation between double groupoids and matched pairs of groups may be extended, or seems to extend, to the triple case. The references give some other occurrences of double groupoids.
This conclusion to the meeting attempts to summarise what we have learnt during the conference (mainly from the review talks) about new observations from Hinode and about theories stimulated by them. Suggestions for future study are also…
Subtraction is a powerful technique for creating new bijections from old. Let's reinvent it! While we're at it, let's reinvent division as well.
We attempt to make superdeterminism more intuitive, notably by simulating a deterministic model system, a billiard game. In this system an initial 'bang' correlates all events, just as in the superdeterministic universe. We introduce the…
We present some new methods for logical deduction, based on ideas from ground theory. Roughly speaking, in our calculi a typical deduction will proceed as follows: we first analyse the premiss down to its ultimate grounds; then we discard…
An interesting line of research in natural language processing (NLP) aims to incorporate linguistic typology to bridge linguistic diversity and assist the research of low-resource languages. While most works construct linguistic similarity…
Infinite sequences are considered in the framework of classical logic from a new point of view.
The goal of this article is to introduce some beautiful known riddles in intuitive topology; hoping to make at least some fun for the reader.
We offer several new summation identities involving harmonic numbers, odd harmonic numbers, and Fibonacci numbers. Our results are derived using three different approaches: partial summation, polynomial identities and binomial…
The main aim of this paper is to establish several Landau-type theorems for certain bounded poly-analytic functions and reduced poly-analytic functions that generalize some previously established results.
A family of congruences interpolating between those of Wilson and Giuga is constructed. Several elementary results are established, in order to present a possible approach to establishing Giuga's conjecture.
We ask questions generalizing uniform versions of conjectures of Mordell and Lang and combining them with the Morton--Silverman conjecture on preperiodic points. We prove a few results relating different versions of such questions.
In this paper we provide an overview of a series of recent results regarding algorithms for searching for subsequences in words or for the analysis of the sets of subsequences occurring in a word.
We survey Kondrat'ev--Landis' conjecture, providing an up-to-date account of the main advances and describing the techniques developed. We complement the overview with references and formulations of the problem in further closely connected…
It is a fundamental property of non-letter Lyndon words that they can be expressed as a concatenation of two shorter Lyndon words. This leads to a naive lower bound log_{2}(n)} + 1 for the number of distinct Lyndon factors that a Lyndon…
Let $n=hw$, where $h$ and $w$ are integers with $h,w \ge 2$. We determine the set of possible intersection numbers of two $n \times n$ latin squares having the additional `Sudoku' constraint based on a $w \times h$ grid of $h \times w$…
Fix a finite alphabet. A necklace is a circular word. For positive integers $n$ and~$k$, a necklace is $(n,k)$-perfect if all words of length $n$ occur $k$ times but at positions with different congruence modulo $k$, for any convention of…
Proof systems for the Relativized Propositional Calculus are defined and compared.
In this paper we present many congruences for several Ap\'ery-like sequences.