nLab
Schur positivity

Contents

Contents

Definition

A symmetric function ff with coefficients in the ground field is Schur positive if, when expanded in the linear basis of Schur polynomials f= μa μs μf = \sum_\mu a_\mu s_\mu, all coefficients a μa_\mu are positive numbers.

References

  • Rebecca Patrias, What is Schur positivity and how common is it? (arXiv:1809.04448)

  • Thomas Lam, Alexander Postnikov, Pavlo Pylyavskyy, Schur positivity and Schur log-concavity, math.CO/0502446

  • James M. Borger, Witt vectors, semirings, and total positivity, arxiv/1310.3013

We extend the big and p-typical Witt vector functors from commutative rings to commutative semirings. In the case of the big Witt vectors, this is a repackaging of some standard facts about monomial and Schur positivity in the combinatorics of symmetric functions. In the p-typical case, it uses positivity with respect to an apparently new basis of the p-typical symmetric functions.

Last revised on April 28, 2021 at 11:53:50. See the history of this page for a list of all contributions to it.