On the interpretation of Whitney numbers through arrangements of hyperplanes, zonotopes, non-Radon partitions, and orientations of graphs
Curtis Greene, Thomas Zasĺavsky · Transactions of the American Mathematical Society · 1983
The doubly indexed Whitney numbers of a finite, ranked partially ordered set L L are (the first kind) w i j = ∑ { μ ( x i , x j ) : x i , x j ∈ L {w_{ij}} = \sum {\{ \mu ({x^i},{x^j}):{x^i},{x^j} \in L} with ranks i , j } i,j\} and (the second kind) W i j = {W_{ij}} = the number of ( x i , x j ) ({x^i},{x^j}) with x i ⩽ x j {x^i} \leqslant {x^j} . When L L has a 0 0 element, the ordinary (simply indexed) Whitney numbers are w j