Related papers: The appearance function for paper-folding words
With the rapid increase in paper submissions to academic conferences, the need for automated and accurate paper-reviewer matching is more critical than ever. Previous efforts in this area have considered various factors to assess the…
In this paper, we will extend the falling and rising factorial transforms \cite{ref. 1} which in this case every arbitrary function can be applied. Then, the properties of these transforms will be investigated and some corollaries will be…
Recently Dekking conjectured the form of the subword complexity function for the Fibonacci-Thue-Morse sequence. In this note we prove his conjecture by purely computational means, using the free software Walnut.
Factors are a foundational component of legal analysis and computational models of legal reasoning. These factor-based representations enable lawyers, judges, and AI and Law researchers to reason about legal cases. In this paper, we…
We regard explanations as a blending of the input sample and the model's output and offer a few definitions that capture various desired properties of the function that generates these explanations. We study the links between these…
A factor $u$ of a word $w$ is a cover of $w$ if every position in $w$ lies within some occurrence of $u$ in $w$. A word $w$ covered by $u$ thus generalizes the idea of a repetition, that is, a word composed of exact concatenations of $u$.…
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…
We explore the Ziv-Lempel and Crochemore factorizations of some classical automatic sequences making an extensive use of the theorem prover Walnut.
A word $u=u_1\dots u_n$ is a scattered factor of a word $w$ if $u$ can be obtained from $w$ by deleting some of its letters: there exist the (potentially empty) words $v_0,v_1,..,v_n$ such that $w = v_0u_1v_1...u_nv_n$. The set of all…
Old and new results for characterizing volume forms in functional integration.
The aim of this note is to give some factorization formulas for different versions of the Macdonald polynomials when the parameter t is specialized at roots of unity, generalizing those existing for Hall-Littlewood functions.
We study the $k$-Bonacci word over the infinite alphabet $\mathbb{N}$. Since the alphabet is infinite, the usual factor complexity is infinite and does not provide any information. We therefore investigate factor occurrence statistics in…
For each integer n, an n-folding curve is obtained by folding n times a strip of paper in two, possibly up or down, and unfolding it with right angles. Generalizing the usual notion of infinite folding curve, we define complete folding…
We introduce a new factorial function which agrees with the usual Euler gamma function at both the positive integers and at all half-integers, but which is also entire. We describe the basic features of this function.
This paper is an extended abstract of the dissertation presented by the author for the doctoral degree in physics and mathematics (in Russia). The main characteristic studied in the dissertation is combinatorial complexity, which is a…
We introduce Peano words, which are words corresponding to finite approximations of the Peano space filling curve. We then find the number of occurrences of certain patterns in these words.
In this position paper, we present a prototype of a visualizer for functional programs. Such programs, whose evaluation model is the reduction of an expression to a value through repeated application of rewriting rules, and which tend to…
We present an exact formula for the number of distinct crease patterns in a square shaped region of a given size that appear in the 2 dimensional paperfolding structure.
Following Inoue et al., we define a word to be a repetition if it is a (fractional) power of exponent at least 2. A word has a repetition factorization if it is the product of repetitions. We study repetition factorizations in several…
A key problem in text summarization is finding a salience function which determines what information in the source should be included in the summary. This paper describes the use of machine learning on a training corpus of documents and…