Geodesic
Pieri's formula for generalized Schur polynomials
Journal of Algebraic Combinatorics, Tome 26 (2007) no. 1, pp. 27-45.

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

Summary: Young's lattice, the lattice of all Young diagrams, has the Robinson-Schensted-Knuth correspondence, the correspondence between certain matrices and pairs of semi-standard Young tableaux with the same shape. Fomin introduced generalized Schur operators to generalize the Robinson-Schensted-Knuth correspondence. In this sense, generalized Schur operators are generalizations of semi-standard Young tableaux. We define a generalization of Schur polynomials as expansion coefficients of generalized Schur operators. We show that the commutation relation of generalized Schur operators implies Pieri's formula for generalized Schur polynomials.
Keywords: keywords Pieri formula, generarized Schur operators, Schur polynomials, Young diagrams, planar binary trees, differential posets, dual graphs, symmetric functions, quasi-symmetric polynomials 
@article{JAC_2007__26_1_a4,
     author = {Numata, Yasuhide},
     title = {Pieri's formula for generalized {Schur} polynomials},
     journal = {Journal of Algebraic Combinatorics},
     pages = {27--45},
     publisher = {mathdoc},
     volume = {26},
     number = {1},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_2007__26_1_a4/}
}
TY  - JOUR
AU  - Numata, Yasuhide
TI  - Pieri's formula for generalized Schur polynomials
JO  - Journal of Algebraic Combinatorics
PY  - 2007
SP  - 27
EP  - 45
VL  - 26
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JAC_2007__26_1_a4/
LA  - en
ID  - JAC_2007__26_1_a4
ER  - 
%0 Journal Article
%A Numata, Yasuhide
%T Pieri's formula for generalized Schur polynomials
%J Journal of Algebraic Combinatorics
%D 2007
%P 27-45
%V 26
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JAC_2007__26_1_a4/
%G en
%F JAC_2007__26_1_a4
Numata, Yasuhide. Pieri's formula for generalized Schur polynomials. Journal of Algebraic Combinatorics, Tome 26 (2007) no. 1, pp. 27-45. http://geodesic.mathdoc.fr/item/JAC_2007__26_1_a4/