 
Summary: Coxeter groups and Hopf algebras I
Marcelo Aguiar and Swapneel Mahajan
Department of Mathematics, Texas A&M University, College Station,
Texas 77843, USA
Email address: maguiar@math.tamu.edu
URL: http://www.math.tamu.edu/maguiar
Department of Mathematics, Indian Institute of Technology, Powai,
Mumbai 400 076, India
Email address: swapneel@math.iitb.ac.in
URL: http://www.math.iitb.ac.in/swapneel
2000 Mathematics Subject Classification. 05E05, 06A11, 06A15, 16W30, 51E24.
Key words and phrases. Coxeter group; descent; global descent; hyperplane
arrangement; left regular band (LRB); projection map; projection poset; lunes; shuffles;
bilinear forms; descent algebra; semisimple; Hopf algebra; (quasi) symmetric functions;
(co)algebra axioms; (nested) set partitions; (nested) set compositions; (co)free
(co)algebra.
Foreword
In the study of a mathematical system, algebraic structures allow for the discovery of
more information. This is the motor behind the success of many areas of mathematics
such as algebraic geometry, algebraic combinatorics, algebraic topology and others. This
