| Autor: |
Avella-Alaminos, Diana, Vallejo, Ernesto |
| Rok vydání: |
2010 |
| Předmět: |
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| Zdroj: |
Discrete Mathematics 312 (2012) 1476-1486 |
| Druh dokumentu: |
Working Paper |
| DOI: |
10.1016/j.disc.2012.01.006 |
| Popis: |
The starting point for this work is an identity that relates the number of minimal matrices with prescribed 1-marginals and coefficient sequence to a linear combination of Kronecker coefficients. In this paper we provide a bijection that realizes combinatorially this identity. As a consequence we obtain an algorithm that to each minimal matrix associates a minimal component, with respect to the dominance order, in a Kronecker product, and a combinatorial description of the corresponding Kronecker coefficient in terms of minimal matrices and tableau insertion. Our bijection follows from a generalization of the dual RSK correspondence to 3-dimensional binary matrices, which we state and prove. With the same tools we also obtain a generalization of the RSK correspondence to 3-dimensional integer matrices. |
| Databáze: |
arXiv |
| Externí odkaz: |
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