Sch\"utzenberger's factorization on the (completed) Hopf algebra of $q-$stuffle product

Chen Bui; G\'erard Henry Edmond Duchamp (LIPN); Vincel Hoang Ngoc Minh (LIPN)

Sch\"utzenberger's factorization on the (completed) Hopf algebra of q-stuffle product

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 1305.4450 v1 pith:7WLSAFQR submitted 2013-05-20 math.CO cs.SC

Sch\"utzenberger's factorization on the (completed) Hopf algebra of q-stuffle product

Chen Bui , G\'erard Henry Edmond Duchamp (LIPN) , Vincel Hoang Ngoc Minh (LIPN) This is my paper

classification math.CO cs.SC

keywords productalgebrafactorizationhopfutzenbergerbasescombinatorialcompleted

verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

0 comments

read the original abstract

In order to extend the Sch\"utzenberger's factorization, the combinatorial Hopf algebra of the $q$-stuffles product is developed systematically in a parallel way with that of the shuffle product and and in emphasizing the Lie elements as studied by Ree. In particular, we will give here an effective construction of pair of bases in duality.

discussion (0)

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

The Antipodes of $q$-Quasi-Symmetric Functions and Non-Commutative Quasi-Symmetric Functions
math.CO 2026-07 accept novelty 6.5

Explicit antipode formulas are proved for commutative and non-commutative q-quasi-symmetric functions, plus a partial antipode on a new fundamental basis of NCQSym, via a cancelation argument that recovers the classic...