From sets to functions: Three elementary examples

A sequence of binomial type is a basis for [x] satisfying a binomial-like identity, e.g. powers, rising and falling factorials. Given two sequences of binomial type, the authors describe a totally combinatorial way of finding the change of basis matrix: to each pair of sequences is associated a poset whose Whitney numbers of the 1st and 2nd kind give the entries of the matrix and its inverse.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/24525/1/0000804.pd