scholarly journals Principal specializations of Schubert polynomials in classical types

2021 ◽  
Vol 4 (2) ◽  
pp. 273-287
Author(s):  
Eric Marberg ◽  
Brendan Pawlowski
Keyword(s):  
Schubert Polynomials

scholarly journals Upper bounds of Schubert polynomials

2021 ◽  
Author(s):  
Neil Jiuyu Fan ◽  
Peter Long Guo
Keyword(s):  
Upper Bounds ◽  
Schubert Polynomials

scholarly journals On the Multiplication of Schubert Polynomials

1998 ◽  
Vol 20 (1) ◽  
pp. 73-97 ◽  
Author(s):  
Rudolf Winkel
Keyword(s):  
Schubert Polynomials

scholarly journals Double Schubert polynomials for the classical groups

2011 ◽  
Vol 226 (1) ◽  
pp. 840-886 ◽  
Author(s):  
Takeshi Ikeda ◽  
Leonardo C. Mihalcea ◽  
Hiroshi Naruse
Keyword(s):  
Classical Groups ◽  
Schubert Polynomials ◽  
Double Schubert Polynomials

scholarly journals Operations on partially ordered sets and rational identities of type A

2013 ◽  
Vol Vol. 15 no. 2 (Combinatorics) ◽  
Author(s):  
Adrien Boussicault
Keyword(s):  
Partially Ordered Sets ◽  
Rational Functions ◽  
Hasse Diagram ◽  
Linear Extensions ◽  
Ordered Sets ◽  
Closed Expression ◽  
Schubert Polynomials ◽  
Special Cases ◽  
The Family ◽  
International Audience

Combinatorics International audience We consider the family of rational functions ψw= ∏( xwi - xwi+1 )-1 indexed by words with no repetition. We study the combinatorics of the sums ΨP of the functions ψw when w describes the linear extensions of a given poset P. In particular, we point out the connexions between some transformations on posets and elementary operations on the fraction ΨP. We prove that the denominator of ΨP has a closed expression in terms of the Hasse diagram of P, and we compute its numerator in some special cases. We show that the computation of ΨP can be reduced to the case of bipartite posets. Finally, we compute the numerators associated to some special bipartite graphs as Schubert polynomials.

scholarly journals Schubert Polynomials and $k$-Schur Functions

10.37236/4139 ◽  
2014 ◽  
Vol 21 (4) ◽  
Author(s):  
Carolina Benedetti ◽  
Nantel Bergeron
Keyword(s):  
Finite Type ◽  
Schur Functions ◽  
Type A ◽  
Bruhat Order ◽  
Schur Function ◽  
Quasisymmetric Functions ◽  
Affine Grassmannian ◽  
Schubert Polynomial ◽  
Schubert Polynomials ◽  
General Program

The main purpose of this paper is to show that the multiplication of a Schubert polynomial of finite type $A$ by a Schur function, which we refer to as Schubert vs. Schur problem, can be understood combinatorially from the multiplication in the space of dual $k$-Schur functions. Using earlier work by the second author, we encode both problems by means of quasisymmetric functions. On the Schubert vs. Schur side, we study the poset given by the Bergeron-Sottile's $r$-Bruhat order, along with certain operators associated to this order. Then, we connect this poset with a graph on dual $k$-Schur functions given by studying the affine grassmannian order of  Lam-Lapointe-Morse-Shimozono. Also, we define operators associated to the graph on dual $k$-Schur functions which are analogous to the ones given for the Schubert vs. Schur problem. This is the first step of our more general program of showing combinatorially  the positivity of the multiplication of a dual $k$-Schur function by a Schur function.

scholarly journals Schubert polynomials and skew Schur functions

1992 ◽  
Vol 14 (2-3) ◽  
pp. 205-210 ◽  
Author(s):  
Axel Kohnert
Keyword(s):  
Schur Functions ◽  
Schubert Polynomials ◽  
Skew Schur Functions

scholarly journals Combinatorial $B_n$-analogues of Schubert polynomials

1996 ◽  
Vol 348 (9) ◽  
pp. 3591-3620 ◽  
Author(s):  
Sergey Fomin ◽  
Anatol N. Kirillov
Keyword(s):  
Schubert Polynomials

Lectures on equivariant Schubert polynomials

2018 ◽  
Author(s):  
Takeshi Ikeda
Keyword(s):  
Schubert Polynomials
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