A Unified Approach to Combinatorial Formulas for Schubert Polynomials

@article{Lenart2004AUA,
  title={A Unified Approach to Combinatorial Formulas for Schubert Polynomials},
  author={C. Lenart},
  journal={Journal of Algebraic Combinatorics},
  year={2004},
  volume={20},
  pages={263-299}
}
  • C. Lenart
  • Published 2004
  • Mathematics
  • Journal of Algebraic Combinatorics
Schubert polynomials were introduced in the context of the geometry of flag varieties. This paper investigates some of the connections not yet understood between several combinatorial structures for the construction of Schubert polynomials; we also present simplifications in some of the existing approaches to this area. We designate certain line diagrams for permutations known as rc-graphs as the main structure. The other structures in the literature we study include: semistandard Young… Expand
30 Citations
Crystal approach to affine Schubert calculus
  • 23
  • PDF
ACTIONS OF THE SYMMETRIC GROUP GENERATED BY COMPARABLE SETS OF INTEGERS AND SMITH INVARIANTS
  • PDF
A Demazure crystal construction for Schubert polynomials
  • 10
  • PDF
A Crystal on Decreasing Factorizations in the 0-Hecke Monoid
  • 3
  • PDF
Maximal Fillings of Moon Polyominoes, Simplicial Complexes, and Schubert Polynomials
  • 41
  • PDF
The Prism tableau model for Schubert polynomials
  • 10
  • PDF
...
1
2
3
...

References

SHOWING 1-10 OF 61 REFERENCES
A Combinatorial Construction of the Schubert Polynomials
  • N. Bergeron
  • Mathematics, Computer Science
  • J. Comb. Theory, Ser. A
  • 1992
  • 24
  • PDF
Diagram Rules for the Generation of Schubert Polynomials
  • R. Winkel
  • Computer Science, Mathematics
  • J. Comb. Theory, Ser. A
  • 1999
  • 21
  • PDF
Balanced Tableaux
  • 131
  • PDF
Skew Schubert polynomials
  • 15
  • PDF
RC-Graphs and Schubert Polynomials
  • 144
  • PDF
The Yang-Baxter equation, symmetric functions, and Schubert polynomials
  • 192
...
1
2
3
4
5
...