On (non-) freeness of some tridendriform algebras

We present some results on the freeness or non freeness of some tridendriform algebras. In particular, we give a combinatorial proof of the freeness of WQSym, an algebra based on packed words, result already known with an algebraic proof. Then, we prove the non-freeness of an another tridendriform a...

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Vydané v:	Discrete mathematics and theoretical computer science Ročník DMTCS Proceedings, 28th...
Hlavný autor:	Vong, Vincent
Médium:	Journal Article Konferenčný príspevok..
Jazyk:	English
Vydavateľské údaje:	DMTCS 22.04.2020 Discrete Mathematics & Theoretical Computer Science
Predmet:	[math.math-co]mathematics [math]/combinatorics [math.co] Combinatorics Mathematics Combinatorics
ISSN:	1365-8050, 1462-7264, 1365-8050
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Popis
Shrnutí:	We present some results on the freeness or non freeness of some tridendriform algebras. In particular, we give a combinatorial proof of the freeness of WQSym, an algebra based on packed words, result already known with an algebraic proof. Then, we prove the non-freeness of an another tridendriform algebra, PQSym, a conjecture remained open. The method of these proofs is generalizable, in particular it has been used to prove the freeness of the dendriform algebra FQSym and the quadrialgebra of 2-permutations.
ISSN:	1365-8050 1462-7264 1365-8050
DOI:	10.46298/dmtcs.6350