{
"id": "1702.08011",
"version": "v1",
"published": "2017-02-26T09:47:06.000Z",
"updated": "2017-02-26T09:47:06.000Z",
"title": "Weak composition quasi-symmetric functions, Rota-Baxter algebras and Hopf algebras",
"authors": [
"Li Guo",
"Jean-Yves Thibon",
"Houyi Yu"
],
"comment": "25 pages",
"categories": [
"math.CO",
"math.RA"
],
"abstract": "We introduce the Hopf algebra of quasi-symmetric functions with semigroup exponents generalizing the Hopf algebra QSym of quasi-symmetric functions. As a special case we obtain the Hopf algebra WCQSym of weak composition quasi-symmetric functions, which provides a framework for the study of a question proposed by G.-C.~Rota relating symmetric type functions and Rota-Baxter algebras. We provide the transformation formulas between the weak composition monomial and fundamental quasi-symmetric functions, which extends the corresponding results for quasi-symmetric functions. Moreover, we show that QSym is a Hopf subalgebra and a Hopf quotient algebra of WCQSym. Rota's question is addressed by identifying WCQsym with the free commutative unitary Rota-Baxter algebra of weight 1 on one generator, which also allows us to equip this algebra with a Hopf algebra structure.",
"revisions": [
{
"version": "v1",
"updated": "2017-02-26T09:47:06.000Z"
}
],
"analyses": {
"subjects": [
"05E05",
"16W99",
"16T33"
],
"keywords": [
"weak composition quasi-symmetric functions",
"free commutative unitary rota-baxter algebra",
"hopf algebra structure",
"relating symmetric type functions",
"hopf algebra qsym"
],
"note": {
"typesetting": "TeX",
"pages": 25,
"language": "en",
"license": "arXiv",
"status": "editable"
}
}
}