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Symmetric Fundamental Expansions to Schur Positivity
Discrete mathematics & theoretical computer science, DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016), DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016) (2020) Cet article a éte moissonné depuis la source Episciences

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We consider families of quasisymmetric functions with the property that if a symmetric function f is a positive sum of functions in one of these families, then f is necessarily a positive sum of Schur functions. Furthermore, in each of the families studied, we give a combinatorial description of the Schur coefficients of f. We organize six such families into a poset, where functions in higher families in the poset are always positive integer sums of functions in each of the lower families. 
@article{DMTCS_2020_special_379_a48,
     author = {Roberts, Austin},
     title = {Symmetric {Fundamental} {Expansions} to {Schur} {Positivity}},
     journal = {Discrete mathematics & theoretical computer science},
     year = {2020},
     volume = {DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016)},
     doi = {10.46298/dmtcs.6366},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.6366/}
}
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Roberts, Austin. Symmetric Fundamental Expansions to Schur Positivity. Discrete mathematics & theoretical computer science, DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016), DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016) (2020). doi: 10.46298/dmtcs.6366

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