Results 11 to 20 of about 41,853 (190)
Affine dual equivalence and $k$-Schur functions [PDF]
Journal of Combinatorics, 2012 The k-Schur functions were first introduced by Lapointe, Lascoux and Morse (2003) in the hopes of refining the expansion of Macdonald polynomials into Schur functions. Recently, an alternative definition for k-Schur functions was given by Lam, Lapointe, Morse, and Shimozono (2010) as the weighted generating function of starred strong tableaux which ...
Sami H. Assaf, Sara C. Billey
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The role of residue and quotient tables in the theory of k-Schur functions [PDF]
Journal of Combinatorial Theory, Series A, 2014 Recently, residue and quotient tables were defined by Fishel and the author, and were used to describe strong covers in the lattice of $k$-bounded partitions. In this paper, we show or conjecture that residue and quotient tables can be used to describe many other results in the theory of $k$-bounded partitions and $k$-Schur functions, including $k ...
Matjaž Konvalinka
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A k-tableau characterization of k-Schur functions [PDF]
Advances in Mathematics, 2005 19 ...
Luc Lapointe, Jennifer Morse
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Schubert Polynomials and $k$-Schur Functions [PDF]
The Electronic Journal of Combinatorics, 2014 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.
Carolina Benedetti, Nantel Bergeron
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Factorization formulas of $K$-$k$-Schur functions II [PDF]
, 2017 28 ...
Motoki Takigiku
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$k$-Schur functions and affine Schubert calculus
, 2013 This book is an exposition of the current state of research of affine Schubert calculus and $k$-Schur functions. This text is based on a series of lectures given at a workshop titled "Affine Schubert Calculus" that took place in July 2010 at the Fields Institute in Toronto, Ontario. The story of this research is told in three parts: 1.
Thomas Lam +5 more
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Expansions of k-Schur Functions in the Affine nilCoxeter Algebra [PDF]
The Electronic Journal of Combinatorics, 2012 We give a type free formula for the expansion of $k$-Schur functions indexed by fundamental coweights within the affine nilCoxeter algebra. Explicit combinatorics are developed in affine type $C$.
Chris Berg +3 more
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k-shape poset and branching of k-Schur functions [PDF]
, 2010 85 ...
Thomas Lam +3 more
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From quantum Schubert polynomials to k-Schur functions via the Toda lattice [PDF]
Mathematical Research Letters, 2010 We show that Lapointe-Lascoux-Morse k-Schur functions (at t=1) and Fomin-Gelfand-Postnikov quantum Schubert polynomials can be obtained from each other by a rational substitution. This is based upon Kostant's solution of the Toda lattice and Peterson's work on quantum Schubert calculus.
Thomas Lam, Mark Shimozono
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Equivariant K-homology of affine Grassmannian and K-theoretic double k-Schur functions [PDF]
We study the torus equivariant K-homology ring of the affine Grassmannian $\mathrm{Gr}_G$ where $G$ is a connected reductive linear algebraic group. In type $A$, we introduce equivariantly deformed symmetric functions called the K-theoretic double $k$-Schur functions as the Schubert bases.
T. Ikeda, M. Shimozono, K. Yamaguchi
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