Abstract: Algebraic combinatorics has, at its core, the study of elements/bases of the ring of symmetric polynomials Sym(n). Obversely,
Lascoux-Schutzenberger introduced numerous asymmetric families in the polynomial ring Pol(n). I will discuss an interpolation between
Sym(n) and Pol(n) in the form of split-symmetric rings. We will see that many important families of polynomials, e.g. the key polynomials and Schubert polynomials, are split-symmetric.
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