Related papers: Sudo-Lyndon
We offer new proofs, refinements as well as new results related to classical means of two variables, including the identric and logarithmic means.
The aim of this paper is to introduce a logic in which nouns and verbs are handled together as a deductive reasoning, and also to observe the relationship between nouns and verbs as well as between logics and conversations.
First introduced in the study of the Sturmian words, the iterated palindromic closure was recently generalized to pseudopalindromes. This operator allows one to construct words with an infinity of pseudopalindromic prefixes, called…
It is a fun game to complete a partial character table of a finite group. We show that one can reconstruct a missing row or column from a given table. The proof relies on deep properties of fully ramified characters. Moreover, we extend a…
This paper enlarges classical syllogistic logic with assertions having to do with comparisons between the sizes of sets. So it concerns a logical system whose sentences are of the following forms: {\sf All $x$ are $y$} and {\sf Some $x$ are…
How can we predict the difficulty of a Sudoku puzzle? We give an overview of difficulty rating metrics and evaluate them on extensive dataset on human problem solving (more then 1700 Sudoku puzzles, hundreds of solvers). The best results…
We announce numerous new results in the theory of orthogonal polynomials on the unit circle.
We collect a number of open questions concerning Diophantine equations, Diophantine Approximation and transcendental numbers. Revised version: corrected typos and added references.
This paper proposes an alternative to standard first-order logic that seeks greater naturalness, generality, and semantic self-containment. The system removes the first-order restriction, avoids type hierarchies, and dispenses with external…
We provide here a dataset for tasks related to natural language understanding and natural language inference. The dataset contains logical puzzles in natural language from three domains: comparing puzzles, knighs and knaves, and zebra…
We present a spoken conversational question answering proof of concept that is able to answer questions about general knowledge from Wikidata. The dialogue component does not only orchestrate various components but also solve coreferences…
Defining the biperiodic Fibonacci words as a class of words over the alphabet $\{0,1\}$, and two specializations the $k-$Fibonacci and classical Fibonacci words, we provide a self-similar decomposition of these words into overlapping words…
This paper presents a new model of WordNet that is used to disambiguate the correct sense of polysemy word based on the clue words. The related words for each sense of a polysemy word as well as single sense word are referred to as the clue…
We introduce new combinatorial objects called the shifted domino tableaux. We prove that these objects are in bijection with pairs of shifted Young tableaux. This bijection shows that shifted domino tableaux can be seen as elements of the…
We propose several Hodge theoretic analogues of the conjectures of Hopf and Singer, and prove them in some special cases.
In this paper, a new approximate syllogistic reasoning schema is described that expands some of the approaches expounded in the literature into two ways: (i) a number of different types of quantifiers (logical, absolute, proportional,…
We introduce ologisms. They generate from ologs by extending their logical expressivity, from the possibility of considering constraints of equational nature only to the possibility of considering constraints of syllogistic nature, in…
New sets (typically found by computer search) with Sidon constant equal to the square root of their cardinalities are given. For each integer $N$ there are only a finite number of groups of prime order containing $N$-element extreme sets.…
In this expository note, we discuss a ``balls-and-urns'' probability puzzle posed by Daniel Litt.
Notes on the Spinpossible puzzle game. We give a mathematical description of the game, prove some elementary bounds on the length of optimal solutions, and consider variations of the game which place restrictions on the set of permitted…