Lattice point generating functions and symmetric cones |
| |
Authors: | Matthias Beck Thomas Bliem Benjamin Braun Carla D. Savage |
| |
Affiliation: | 1. Department of Mathematics, San Francisco State University, San Francisco, CA, 94132, USA 2. Kempener Str. 57, 50733, K?ln, Germany 3. Department of Mathematics, University of Kentucky, Lexington, KY, 40506-0027, USA 4. Department of Computer Science, North Carolina State University, Raleigh, NC, 27695-8206, USA
|
| |
Abstract: | We show that a recent identity of Beck–Gessel–Lee–Savage on the generating function of symmetrically constrained compositions of integers generalizes naturally to a family of convex polyhedral cones that are invariant under the action of a finite reflection group. We obtain general expressions for the multivariate generating functions of such cones, and work out their general form more specifically for all symmetry groups of type A (previously known) and types B and D (new). We obtain several applications of these expressions in type B, including identities involving permutation statistics and lecture hall partitions. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|