Abstract
The integers W 0 , ..., W t are called Whitney numbers of the second kind for a ranked poset if W k is the number of elements of rank k . The set of transpositions T = {(1, n ), (2, n ), ..., ( n - 1, n )} generates S n , the symmetric group. We define the star poset, a ranked poset the elements of which are those of S n and the partial order of which is obtained from the Cayley graph using T . We characterize minimal factorizations of elements of S n as products of generators in T and provide recurrences, generating functions and explicit formulae for the Whitney numbers of the second kind for the star poset.
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