In this paper, a direct combinatorial proof is given of a result on permutation pairs originally due to Carlitz, Scoville, and Vaughan and later extended. It concerns showing that the series expansion of the reciprocal of a certain multiply exponential generating function has positive integer coefficients. The arguments may then be applied to related problems, one of which concerns the reciprocal of the exponential series for Fibonacci numbers.
|Number of pages||10|
|Journal||Central European Journal of Mathematics|
|State||Published - Apr 2012|
- Combinatorial proof
- Exponential generating function
ASJC Scopus subject areas
- Mathematics (all)