semimodular, Exact enumeration problems, generating functions, semimodular lattice, left-modular elements, supersolvable, Combinatorial aspects of matroids and geometric lattices, Semimodular lattices, geometric lattices, shuffle posets, left-modular, Theoretical Computer Science, Combinatorics of partially ordered sets, Computational Theory and Mathematics, factorization, Discrete Mathematics and Combinatorics, modular, characteristic polynomial, partition lattices, supersolvability, modularity, Möbius functions, lattice