For a bounded and graded poset , we show that if is EL-shellable, then so is its -fold Segre power ( factors), as defined by Björner and Welker [J. Pure Appl. Algebra, 198(1-3), 43--55 (2005)]. Our EL-labeling leads to formulas for the rank-selected invariants of , generalising those given by Stanley for the subspace lattice [J. Combinatorial Theory Ser. A, 20(3):336-356, 1976].
