Geodesic
Linearly independent products of rectangularly complementary Schur functions
The electronic journal of combinatorics, Tome 9 (2002)
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Fix a rectangular Young diagram $R$, and consider all the products of Schur functions $s_\lambda s_\lambda^{c}$, where $\lambda$ and $\lambda^{c}$ run over all (unordered) pairs of partitions which are complementary with respect to $R$. Theorem: The self-complementary products, $s_\lambda^2$ where $\lambda=\lambda^{c}$, are linearly independent of all other $s_\lambda s_\lambda^{c}$. Conjecture: The products $s_\lambda s_\lambda^{c}$ are all linearly independent.
DOI : 10.37236/1655
Classification : 05E05
Mots-clés : Schur functions, rectangular Young diagram 
@article{10_37236_1655,
     author = {Michael Kleber},
     title = {Linearly independent products of rectangularly complementary {Schur} functions},
     journal = {The electronic journal of combinatorics},
     year = {2002},
     volume = {9},
     doi = {10.37236/1655},
     zbl = {1013.05088},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1655/}
}
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Michael Kleber. Linearly independent products of rectangularly complementary Schur functions. The electronic journal of combinatorics, Tome 9 (2002). doi: 10.37236/1655

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