A Timed Version of the Plactic Monoid

TL;DR

This paper extends classical combinatorial structures like tableaux, insertion algorithms, and the plactic monoid to the setting of timed words with timestamps, and adapts key theorems and algorithms to this new context.

Contribution

It introduces a timed version of the plactic monoid, extending fundamental combinatorial concepts and algorithms to words with timestamps, and proves Greene's theorem for this setting.

Findings

Greene's theorem is formulated and proved for timed words.

Algorithms for RSK correspondence are extended to real matrices.

Foundations for combinatorics with timed words are established.

Abstract

Timed words are words where letters of the alphabet come with time stamps. We extend the definitions of semistandard tableaux, insertion, Knuth equivalence, and the plactic monoid to the setting of timed words. Using this, Greene's theorem is formulated and proved for timed words, and algorithms for the RSK correspondence are extended to real matrices.