The equations DkY = Xn in combinatorial species

✍ Scribed by Dayanand S. Rajan

• Publisher: Elsevier Science
• Year: 1993
• Tongue: English
• Weight: 632 KB
• Volume: 118
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/0012-365x(93)90061-w

✦ Synopsis

Rajan, D.S., The equations Dk Y= X" in combinatorial species, Discrete Mathematics 118 (1993) 197-206.

The category of combinatorial species was introduced by Joyal, and has been studied extensively by him and others. This category is equipped with a derivative operation (endofunctor). This allows one to differentiate species in a manner similar to differentiating power series. We solve, completely, the family of differential equations Dky = X" for species. For this, we use results on the conjugacy classes of sharply k-transitive groups. We provide, also, a new proof of a sharpened version of Zassenhaus' theorem on sharply 2-transitive groups of type I.