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International Journal of Mathematics and Mathematical Sciences
Volume 2003, Issue 24, Pages 1497-1508
http://dx.doi.org/10.1155/S0161171203209303

The derangement problem relative to the Mahonian process

Mathematics Department, California Polytechnic State University, San Luis Obispo, CA 93407, USA

Received 23 September 2002

Copyright © 2003 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We survey n! plus q-derangement problems. Solutions to four Mahonian statistics arising in connection with cycle placement rules are presented. A few conjectures are also made.