Minimal Factorizations of a Cycle and Central Multiplicative Functions on the Infinite Symmetric Group

✍ Scribed by Philippe Biane

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 508 KB
• Volume: 76
• Category: Article
• ISSN: 0097-3165
• DOI: 10.1006/jcta.1996.0101

✦ Synopsis

We show that the number of factorizations _=/ 1 } } } / r of a cycle of length n into a product of cycles of lengths a 1 , ..., a r , with r j=1 (a j &1)=n&1, is equal to n r&1 . This generalizes a well known result of J. Denes, concerning factorizations into a product of transpositions. We investigate some consequences of this result, for central multiplicative functions on the infinite symmetric group, and use them to give a new proof of a recent result of A. Nica and R. Speicher on non-crossing partitions.