A Derangement Problem.
Abstract
Even and Gillis found a closed form solution to a derangement problem of (n sub 1) + ... + (n sub k) objects where (n sub i) objects are of type i. Their solution was an integral of products of Laguerre polynomials. A new derivation is given using MacMahon's master theorem and an asymptotic agrument is given to estimate the size of the number of derangements when (n sub 1 = ... = (n sub k) and k is large. The authors also show how Even and Gillis' integral representation follows easily from Kaplansky's symbolic representation of these numbers.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 01, 1975
- Accession Number
- ADA016101
Entities
People
- Mourad Ismail
- Richard Askey
- Thanaa Rashed
Organizations
- University of Wisconsin–Madison