Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4647551 | Discrete Mathematics | 2013 | 12 Pages |
Abstract
Stirling numbers and Bessel numbers have a long history, and both have been generalized in a variety of directions. Here, we present a second level generalization that has both as special cases. This generalization often preserves the inverse relation between the first and second kind, and has simple combinatorial interpretations. We also frame the discussion in terms of the exponential Riordan group. Then the inverse relation is just the group inverse, and factoring inside the group leads to many results connecting the various Stirling and Bessel numbers.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Gi-Sang Cheon, Ji-Hwan Jung, Louis W. Shapiro,