A DECOMPOSITION OF SCHUR FUNCTIONS AND AN ANALOGUE OF THE ROBINSON-SCHENSTED-KNUTH ALGORITHM
By Sarah K. Mason. 2006
57 citations recorded by the source corpus.
We exhibit a weight-preserving bijection between semi-standard Young tableaux and semi-skyline augmented fillings to provide a combinatorial proof that the Schur functions decompose into nonsymmetric functions indexed by compositions. The insertion procedure involved in the proof leads to an analogue of the Robinson-Schensted- Knuth Algorithm for semi-skyline augmented fillings. This procedure commutes with the Robinson-Schensted-Knuth Algorithm, and therefore retains many of its properties.
Subfields: Discrete Mathematics and Combinatorics, Spectroscopy, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/c3799f71722b23432784cd86cc2609694d9b9070
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Citations in the corpus
- An explicit construction of type A Demazure atoms (2007, methodology): “4 of [10] states that these conditions are enough to guarantee that the filling is non-attacking.”
- Recent Trends in Quasisymmetric Functions (2018, methodology): “The Demazure atoms decompose the Schur functions in a natural way and their generating diagrams satisfy a Robinson-Schensted-Knuth-style algorithm [91].”
- The q, t-Catalan numbers and the space of diagonal harmonics : with an appendix on the combinatorics of Macdonald polynomials (2007, methodology): “Sarah Mason has proved this identity bijectively by developing a generalization of the RSK algorithm [Mas06], [Mas].”