Symmetric Fundamental Expansions to Schur Positivity
1 : Highline College, Des Moines, WA
2 : 1QBit Information Technologies, Vancouver, BC
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.
- Poster