Abstract
Schur polynomials are a special case of Schubert polynomials. In this paper, we give an algorithm to compute the product of a Schubert polynomial with a Schur polynomial on the basis of Schubert polynomials. This is a special case of the general problem of the multiplication of two Schubert polynomials, where the corresponding algorithm is still missing. The main tools for the given algorithm is a factorization property of a special class of Schubert polynomials and the transition formula for Schubert polynomials.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
N. Bergeron and S. Billey, RC-graphs and Schubert polynomials, Experimental Mathematics2 (1993) 257–269.
S. Fomin and A.N. Kirillov, The Young-Baxter equation, symmetric functions and Schubert polynomials. Discrete Math.15 (1996) 123–143.
A. Kohnert, Weintrauben, Polynome, Tableaux, Bayreuther Mathematische Schriften38 (1990) 1–97.
A. Kohnert, Schubert polynomials and skew Schur functions, J. Symbolic Computation14 (1992) 205–210.
A. Lascoux and M.P. Schützenberger, Classes de Chern des variétés de drapeaux, C.R. Acad. Sc. Paris294 (1982) 393–398.
A. Lascoux and M.P. Schützenberger, Schubert polynomials and the Littlewood-Richardson rule, Letters in Mathematical Physics10 (1985) 111–124.
D. Monk, Geometry of flag manifolds, Proc. London Math. Soc. (3)9 (1959) 253–286.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Kohnert, A. Multiplication of a Schubert polynomial by a Schur polynomial. Annals of Combinatorics 1, 367–375 (1997). https://doi.org/10.1007/BF02558487
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02558487