Skip to main content
We gratefully acknowledge support from the Simons Foundation, member institutions, and all contributors. Donate
arXiv logo
Cornell University Logo

Mathematics > Combinatorics

arXiv:1804.09735 (math)
[Submitted on 25 Apr 2018 (v1), last revised 30 Jan 2019 (this version, v2)]

Title:Nyldon words

Authors:Émilie Charlier, Manon Philibert, Manon Stipulanti
View PDF
Abstract:The Chen-Fox-Lyndon theorem states that every finite word over a fixed alphabet can be uniquely factorized as a lexicographically nonincreasing sequence of Lyndon words. This theorem can be used to define the family of Lyndon words in a recursive way. If the lexicographic order is reversed in this definition, we obtain a new family of words, which are called the Nyldon words. In this paper, we show that every finite word can be uniquely factorized into a lexicographically nondecreasing sequence of Nyldon words. Otherwise stated, Nyldon words form a complete factorization of the free monoid with respect to the decreasing lexicographic order. Then we investigate this new family of words. In particular, we show that Nyldon words form a right Lazard set.
Comments: 28 pages
Subjects: Combinatorics (math.CO); Discrete Mathematics (cs.DM)
MSC classes: 68R15, 94A45
Cite as: arXiv:1804.09735 [math.CO]
  (or arXiv:1804.09735v2 [math.CO] for this version)
  https://doi.org/10.48550/arXiv.1804.09735

Submission history

From: Manon Stipulanti [view email]
[v1] Wed, 25 Apr 2018 18:13:51 UTC (44 KB)
[v2] Wed, 30 Jan 2019 19:16:11 UTC (45 KB)
Full-text links:

Access Paper:

view license
Current browse context:
math.CO
< prev   |   next >
new | recent | 2018-04
Change to browse by:
cs
cs.DM
math

References & Citations

1 blog link

(what is this?)
export BibTeX citation

Bookmark

BibSonomy logo Reddit logo

Bibliographic and Citation Tools

Bibliographic Explorer (What is the Explorer?)
Connected Papers (What is Connected Papers?)
Litmaps (What is Litmaps?)
scite Smart Citations (What are Smart Citations?)

Code, Data and Media Associated with this Article

alphaXiv (What is alphaXiv?)
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub (What is DagsHub?)
Gotit.pub (What is GotitPub?)
Hugging Face (What is Huggingface?)
Papers with Code (What is Papers with Code?)
ScienceCast (What is ScienceCast?)

Demos

Replicate (What is Replicate?)
Hugging Face Spaces (What is Spaces?)
TXYZ.AI (What is TXYZ.AI?)

Recommenders and Search Tools

Influence Flower (What are Influence Flowers?)
CORE Recommender (What is CORE?)

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.

Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)