Mutually describing multisets and integer partitions |
| |
Authors: | Shalom Eliahou Martin J Erickson |
| |
Institution: | 1. Univ Lille Nord de France, F-59000 Lille, France;2. ULCO, LMPA J. Liouville, B.P. 699, F-62228 Calais, France;3. CNRS, FR 2956, France;4. Department of Mathematics and Computer Science, Truman State University, Kirksville, MO 63501, USA |
| |
Abstract: | To each finite multiset , with underlying set , we associate a new multiset , obtained by adjoining to the multiplicities of its elements in . We study the orbits of the map under iteration, and show that if consists of nonnegative integers, then its orbit under converges to a cycle. Moreover, we prove that all cycles of over are of length at most , and we completely determine them. This amounts to finding all systems of mutually describing multisets. In the process, we are led to introduce and study a related discrete dynamical system on the set of integer partitions of for each . |
| |
Keywords: | |
本文献已被 ScienceDirect 等数据库收录! |
|