Geodesic
Trees, set compositions and the twisted descent algebra
Journal of Algebraic Combinatorics, Tome 28 (2008) no. 1, pp. 3-23.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We first show that increasing trees are in bijection with set compositions, extending simultaneously a recent result on trees due to Tonks and a classical result on increasing binary trees. We then consider algebraic structures on the linear span of set compositions (the twisted descent algebra). Among others, a number of enveloping algebra structures are introduced and studied in detail. For example, it is shown that the linear span of trees carries an enveloping algebra structure and embeds as such in an enveloping algebra of increasing trees. All our constructions arise naturally from the general theory of twisted Hopf algebras.
Keywords: keywords increasing tree, set composition, descent algebra, twisted Hopf algebra 
@article{JAC_2008__28_1_a10,
     author = {Patras, Fr\'ed\'eric and Schocker, Manfred},
     title = {Trees, set compositions and the twisted descent algebra},
     journal = {Journal of Algebraic Combinatorics},
     pages = {3--23},
     publisher = {mathdoc},
     volume = {28},
     number = {1},
     year = {2008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_2008__28_1_a10/}
}
TY  - JOUR
AU  - Patras, Frédéric
AU  - Schocker, Manfred
TI  - Trees, set compositions and the twisted descent algebra
JO  - Journal of Algebraic Combinatorics
PY  - 2008
SP  - 3
EP  - 23
VL  - 28
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JAC_2008__28_1_a10/
LA  - en
ID  - JAC_2008__28_1_a10
ER  - 
%0 Journal Article
%A Patras, Frédéric
%A Schocker, Manfred
%T Trees, set compositions and the twisted descent algebra
%J Journal of Algebraic Combinatorics
%D 2008
%P 3-23
%V 28
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JAC_2008__28_1_a10/
%G en
%F JAC_2008__28_1_a10
Patras, Frédéric; Schocker, Manfred. Trees, set compositions and the twisted descent algebra. Journal of Algebraic Combinatorics, Tome 28 (2008) no. 1, pp. 3-23. http://geodesic.mathdoc.fr/item/JAC_2008__28_1_a10/