Complexity of tropical Schur polynomials
Résumé
We study the complexity of computation of a tropical Schur polynomial T s λ where λ is a partition, and of a tropical polynomial T m λ obtained by the tropicalization of the monomial symmetric function m λ. Then T s λ and T m λ coincide as tropical functions (so, as convex piece-wise linear functions), while differ as tropical polynomials. We prove the following bounds on the complexity of computing over the tropical semi-ring (R, max, +): • a polynomial upper bound for T s λ and • an exponential lower bound for T m λ. Also the complexity of tropical skew Schur polynomials is discussed.
Domaines
Mathématiques [math]
Origine : Fichiers produits par l'(les) auteur(s)