9
votes
Accepted
"Nyldon words": understanding a class of words factorizing the free monoid increasingly
My co-authors (Émilie Charlier, Manon Philibert) and I give positive answers to Grinberg's conjectures in the paper E. Charlier, M. Philibert, M. Stipulanti, Nyldon words. So it is true that there are ...
- 106
2
votes
Accepted
The shuffle algebra over the rationals is isomorphic to the polynomial algebra in the Lyndon words
This is proven in Theorem 6.3.4 of Hopf Algebras in Combinatorics
by Grinberg and Reiner.
They call it "Radford’s theorem on the shuffle algebra" citing Theorem 3.1.1(e) of A natural ring ...
- 7,875
1
vote
Accepted
Cliques in overlap graphs for words
At least one of the questions admit counterexamples. Namely, let $\Sigma = \{a, b, c, d \}$, and $S = \{ ab^nc d ab^mc : n > m \}$. Then all words in $S$ are Lyndon, $OG(S)$ is triangle-free and ...
- 435
1
vote
Lyndon words and Hall basis
There is no simple connection. Note that there are many different Hall sets H. The Lyndon basis is not such a Hall basis.
However, one can easily relax the ...
- 380
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