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Combinatorics of the free Baxter algebra Marcelo Aguiar
 

Summary: Combinatorics of the free Baxter algebra
Marcelo Aguiar
Department of Mathematics
Texas A&M University, College Station, TX, USA
maguiar@math.tamu.edu
Walter Moreira
Department of Mathematics
Texas A&M University, College Station, TX, USA
wmoreira@math.tamu.edu
Submitted: October 7, 2005; Accepted: February 9, 2006
Mathematics Subject Classification: 05A15, 08B20, 16W99
Abstract
We study the free (associative, non-commutative) Baxter algebra on one gen-
erator. The first explicit description of this object is due to Ebrahimi-Fard and
Guo. We provide an alternative description in terms of a certain class of trees,
which form a linear basis for this algebra. We use this to treat other related cases,
particularly that in which the Baxter map is required to be quasi-idempotent, in a
unified manner. Each case corresponds to a different class of trees.
Our main focus is on the underlying combinatorics. In several cases, we pro-
vide bijections between our various classes of trees and more familiar combinatorial

  

Source: Aguiar, Marcelo - Department of Mathematics, Texas A&M University

 

Collections: Mathematics