par Lunts, Valery;Spenko, Špela 
;Van Den Bergh, Michel
Référence Pure and Applied Mathematics Quarterly, 20, 3, page (1433-1458)
Publication Publié, 2024-07-01
;Van Den Bergh, MichelRéférence Pure and Applied Mathematics Quarterly, 20, 3, page (1433-1458)
Publication Publié, 2024-07-01
Article révisé par les pairs
| Résumé : | We find an explicit Sn-equivariant bijection between the integral points in a certain zonotope in Rn, combinatorially equivalent to the permutahedron, and the set of m-parking functions of length n. This bijection restricts to a bijection between the regular Sn-orbits and (m, n)-Dyck paths, the number of which is given by the Fuss-Catalan number An (m, 1). Our motivation came from studying tilting bundles on noncommutative Hilbert schemes. As a side result we use these tilting bundles to construct a semi-orthogonal decomposition of the derived category of noncommutative Hilbert schemes. |
