Geodesic
Recursive and Combinatorial Properties of Schubert Polynomials
Séminaire lotharingien de combinatoire, Tome 38 (1996)

Voir la notice de l'acte provenant de la source Séminaire Lotharingien de Combinatoire website

We describe two recursive methods for the calculation of Schubert polynomials and use them to give new relatively simple proofs of their basic properties. Moreover, we present (1) methods for the calculation of a reduced word for a permutation from its Lehmer code (and other small algorithms for the manipulation of Lehmer codes), (2) new determinantal formulas for certain Schubert polynomials, which `interpolate' the well known formulas for Schur polynomials, and (3) a fast and simple method for the recursive calculation of Schubert polynomials avoiding divided differences (thereby avoiding completely the computation of intermediary terms, which eventually cancel). The paper can be read as a short self contained introduction to Schubert polynomials providing full proofs. 

@article{SLC_1996_38_a3,
     author = {Rudolf Winkel},
     title = {Recursive and {Combinatorial} {Properties} of {Schubert} {Polynomials}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {38},
     year = {1996},
     url = {http://geodesic.mathdoc.fr/item/SLC_1996_38_a3/}
}
TY  - JOUR
AU  - Rudolf Winkel
TI  - Recursive and Combinatorial Properties of Schubert Polynomials
JO  - Séminaire lotharingien de combinatoire
PY  - 1996
VL  - 38
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SLC_1996_38_a3/
ID  - SLC_1996_38_a3
ER  - 
%0 Journal Article
%A Rudolf Winkel
%T Recursive and Combinatorial Properties of Schubert Polynomials
%J Séminaire lotharingien de combinatoire
%D 1996
%V 38
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SLC_1996_38_a3/
%F SLC_1996_38_a3
Rudolf Winkel. Recursive and Combinatorial Properties of Schubert Polynomials. Séminaire lotharingien de combinatoire, Tome 38 (1996). http://geodesic.mathdoc.fr/item/SLC_1996_38_a3/