Using Schubert basis to compute with multivariate polynomials

Advances in Applied Mathematics

Volumn 19, Issue 1, 1997, Pages 45-60

  Kohnert, Axel ^a   Veigneau, Sébastien ^b  

^a UNIVERSITY OF BAYREUTH   (Germany)

^b Université de Marne la Vallée   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031188348     PISSN: 01968858     EISSN: None     Source Type: Journal    
DOI: 10.1006/aama.1997.0526     Document Type: Article

References (18)

1. Bernstein I. N., Gelfand I. M., Gelfand S. I. Schubert cells and cohomology of the spacesGP. Uspekhi. Mat. Nauk. 28:1973;3-26.
2. Demazure M. Désingularisation des variétés de Schubert. Annales de l'École Normale Supérieure. 6:1974;163-172.
3. S. Fomin, C. Greene, 1995, Noncommutative Schur functions and their applications.
4. S. Fomin, A. Kirillov, Yang-Baxter equation, symmetric functions and Schubert polynomials, Proceedings, 5th Conference, Formal Power Series and Algebraic Combinatorics, Florence, 1993, 215, 229.
5. Fulton W. Flags, Schubert polynomials, degeneracy loci and determinantal formulas. Duke Math. J. 65:1991;381-420.
6. Fulton W., Lascoux A. A Pieri formula in the Grothendieck ring of a flag bundle. Duke Math. J. 76:1994;711-729.
7. Gelfand I. M., Krob D., Lascoux A., Leclerc B., Retakh V. S., Thibon J.-Y. Noncommutative symmetric functions. Adv. in Math. 112:1995;218-348.
8. Kerber A., Kohnert A., Lascoux A. SYMMETRICA, an object oriented computer algebra system for the symmetric group. J. Symbolic Comput. 14:1992;195-203.
9. Kohnert A. Weintrauben, Polynome, Tableaux. Bayreuther Math. Schr. 38:1991;1-97.
10. Lascoux A., Schützenberger M. P. Schubert polynomials and the Littlewood-Richardson Rule. Lett. Math. Phys. 10:1985;111-124.
11. Lascoux A., Schützenberger M. P. Symmetry and Flag manifolds. Lect. Notes in Math. 996:1983;Springer-Verlag, New York/Berlin. p. 118-144.
12. Lascoux A. Classes de Chern des variétés de drapeaux. C.R. Acad. Sci. Paris. 295:1982;393-398.
13. Lascoux A., Schützenberger M. P. Structure de Hopf de l'anneau de cohomologie et de l'anneau de Grothendieck d'une variété de drapeaux. C.R. Acad. Sci. Paris. 295:1982;629-633.
14. Lascoux A., Schützenberger M. P. Interpolation de Newton à plusieurs variables. Lect. Notes in Math. 1146:1983-84;Springer-Verlag, New York/Berlin.
15. Macdonald I. G. Notes on Schubert Polynomials. Publ. LACIM. 6:1991;UQAM, Montréal.
16. Macdonald I. G. Symmetric Functions and Hall Polynomials. 1995;Clarendon Press, Oxford.
17. Monk D. The Geometry of flag manifolds. Proc. London Math. Soc. (3). 9:1959;253-286.
18. B. C. V. Ung, S. Veigneau, ACE, un environnement de calcul en Combinatoire Algébrique, Proceedings, 7th Conference, Formal Power Series and Algebraic Combinatorics, Université de Marne-la-Vallée, 1995, 557, 562.