Quasi-shuffle products
| dc.creator | Hoffman, Michael E. | |
| dc.date | 1999-07-27 | |
| dc.date.accessioned | 2026-07-07T05:30:05Z | |
| dc.date.available | 2026-07-07T05:30:05Z | |
| dc.description | Given a locally finite graded set A and a commutative, associative operation on A that adds degrees, we construct a commutative multiplication * on the set of noncommutative polynomials in A which we call a quasi-shuffle product; it can be viewed as a generalization of the shuffle product. The resulting commutative algebra can be given the structure of a Hopf algebra (_A_,*,Delta). In the case where A is the set of positive integers and the operation on A is addition, (_A_,*,Delta) is the Hopf algebra of quasi-symmetric functions. If rational coefficients are allowed, there is a Hopf algebra isomorphism exp from the shuffle Hopf algebra on A onto (_A_,*,Delta). We discuss the dual of (_A_,*,Delta), and define a deformation *_q of * that coincides with * when q = 1 and is isomorphic to the concatenation product when q is not a root of unity. Finally, we discuss various examples of this construction. | |
| dc.description | 18 pages. See also http://www.nadn.navy.mil/Users/math/meh/research.html | |
| dc.identifier | https://arxiv.org/abs/math/9907173 | |
| dc.identifier | http://arxiv.org/abs/math/9907173 | |
| dc.identifier | J. Algebraic Combin. 11 (2000), 49-68. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/78883 | |
| dc.subject | Quantum Algebra | |
| dc.subject | Combinatorics | |
| dc.subject | 16W30 (Primary); 05E05 (Secondary) | |
| dc.title | Quasi-shuffle products | |
| dc.type | text |