# A bijection on core partitions and a parabolic quotient of the affine symmetric group

@article{Berg2008ABO, title={A bijection on core partitions and a parabolic quotient of the affine symmetric group}, author={Chris Berg and Brant C. Jones and Monica Vazirani}, journal={J. Comb. Theory, Ser. A}, year={2008}, volume={116}, pages={1344-1360} }

## 21 Citations

### Bijective projections on parabolic quotients of affine Weyl groups

- Mathematics
- 2012

Affine Weyl groups and their parabolic quotients are used extensively as indexing sets for objects in combinatorics, representation theory, algebraic geometry, and number theory. Moreover, in the…

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The k-Schur functions were first introduced by Lapointe, Lascoux and Morse [18] in the hopes of refining the expansion of Macdonald polynomials into Schur functions. Recently, an alternative…

### ($\ell,0)$-Carter partitions, a generating function, and their crystal theoretic interpretation

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The main theorem is the equivalence of the combinatoric and the one introduced by James and Mathas of the "$(\ell,0)$-JM partitions" (see \cite{F}) that are also $\ell$-regular".

### Affine symmetric group

- Mathematics
- 2021

The affine symmetric group is a mathematical structure that describes the symmetries of the number line and the regular triangular tesselation of the plane, as well as related higher dimensional…

### Applying parabolic Peterson: affine algebras and the quantum cohomology of the Grassmannian

- MathematicsJournal of Combinatorics
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The Peterson isomorphism relates the homology of the affine Grassmannian to the quantum cohomology of any flag variety. In the case of a partial flag, Peterson's map is only a surjection, and one…

### A bijection between (bounded) dominant Shi regions and core partitions

- Mathematics
- 2010

It is well-known that Catalan numbers $C_n = \frac{1}{ n+1} \binom{2n}{n}$ count the number of dominant regions in the Shi arrangement of type $A$, and that they also count partitions which are both…

### k-Schur Functions and Affine Schubert Calculus

- Mathematics
- 2014

Author(s): Lam, T; Morse, J; Shimozono, M; Lapointe, L; Schilling, A; Zabrocki, M | Abstract: This book is an exposition of the current state of research of affine Schubert calculus and $k$-Schur…

### A core model for G2

- MathematicsInvolve, a Journal of Mathematics
- 2021

The action of the affine Weyl group of type A n on its coroot lattice is classically modeled using n -cores, which are integer partitions with no hooks of length n . Exploiting an identification…

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