Knuth's Moves on Timed Words

TL;DR

This paper explains Schensted's algorithm and Greene's extension for ordered words, and introduces a new generalization of these results to timed words, expanding their applicability.

Contribution

It presents a novel generalization of Schensted's and Greene's results to timed words, extending classical combinatorial algorithms.

Findings

Extended Schensted's algorithm to timed words

Generalized Greene's results for timed words

Provides a framework for analyzing timed words using combinatorial methods

Abstract

We give an exposition of Schensted's algorithm to find the length of the longest increasing subword of a word in an ordered alphabet, and Greene's generalization of Schensted's results using Knuth equivalence. We announce a generalization of these results to timed words.