Abelian Combinatorics on Words: a Survey

07/20/2022
by   Gabriele Fici, et al.
0

We survey known results and open problems in abelian combinatorics on words. Abelian combinatorics on words is the extension to the commutative setting of the classical theory of combinatorics on words, i.e., the extension based on the equivalence relation defined in the set of words by having the same Parikh vector, that is, the same number of occurrences of each letter of the alphabet – called abelian equivalence. In the past few years, there was a lot of research on abelian analogues of classical definitions and properties in combinatorics on words. This survey aims to gather these results.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
06/12/2018

A Timed Version of the Plactic Monoid

Timed words are words where letters of the alphabet come with time stamp...
research
06/09/2019

Borders, Palindrome Prefixes, and Square Prefixes

We show that the number of length-n words over a k-letter alphabet havin...
research
09/09/2018

Well Quasiorders and Hierarchy Theory

We discuss some applications of WQOs to several fields were hierarchies ...
research
11/06/2018

Knuth's Moves on Timed Words

We give an exposition of Schensted's algorithm to find the length of the...
research
12/07/2022

Cocke–Younger–Kasami–Schwartz–Zippel algorithm and relatives

The equivalence problem for unambiguous grammars is an important, but ve...
research
07/17/2018

Parikh Motivated Study on Repetitions in Words

We introduce the notion of general prints of a word, which is substantia...
research
05/04/2021

Simulation by Rounds of Letter-to-Letter Transducers

Letter-to-letter transducers are a standard formalism for modeling react...

Please sign up or login with your details

Forgot password? Click here to reset