A New Decomposition of Derangements

✍ Scribed by Dongsu Kim; Jiang Zeng

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 105 KB
• Volume: 96
• Category: Article
• ISSN: 0097-3165
• DOI: 10.1006/jcta.2001.3190

✦ Synopsis

We give a new decomposition of derangements, which gives a direct interpretation of a formula for their generating function. This decomposition also works for counting derangements by number of excedances.

2001 Academic Press

Of course (1) can be proved by various methods, but, as pointed out by Gessel [4], it seems difficult to directly interpret (1) (even in the x=1