We show that the self-shuffle of Thue-Morse given by Charlier et al. is optimal/canonical in the sense that among self-shuffles of Thue-Morse, it has the lexicographically least directive sequence starting with 1.

Applied researchers using kernel density estimation have worked with optimal bandwidth rules that invariably assumed the reference is Normal (optimal only if true underlying Normal). We offer four new rules-of-thumb based on other infinitely supported distributions: Logistic, Laplace, Student's t and Asymmetric Laplace. Additionally, we propose a psuedo rule-of-thumb (ROT) Gram-Charlier expansi...

Grinberg defined Nyldon words as those which cannot be factorized into a sequence of lexicographically nondecreasing smaller words. He was inspired by Lyndon words, the same way except with "nondecreasing" replaced "nonincreasing." Charlier, Philibert, and Stipulanti proved that, like any word has unique factorization They also show that form right Lazard set, equivalently, Hall set. In this pa...

Abstract The main aim of this paper is to define and investigate more general multiple Charlier polynomials on the linear lattice $\omega \mathbb{N} = \{ 0,\omega ,2\omega ,\ldots \} $ ω N = { 0 , 2 … <m...