Enumerative combinatorics
Journal of Combinatorial Theory Series A
Direct sum decompositions of matroids and exponential structures
Journal of Combinatorial Theory Series B
The Homology of Partitions with an Even Number of Blocks
Journal of Algebraic Combinatorics: An International Journal
Subspace Arrangements of Type Bn and Dn
Journal of Algebraic Combinatorics: An International Journal
The r-cubical lattice and a generalization of the cd-index
European Journal of Combinatorics
Partitions with Restricted Block Sizes, Möbius Functions, and the k-of-Each Problem
SIAM Journal on Discrete Mathematics
Whitney Homology of Semipure Shellable Posets
Journal of Algebraic Combinatorics: An International Journal
Regular Article: Cohomology of Dowling Lattices and Lie (Super)Algebras
Advances in Applied Mathematics
The (co)homology of lattices of partitions with restricted block size
The (co)homology of lattices of partitions with restricted block size
On the Homology of the h,k-Equal Dowling Lattice
SIAM Journal on Discrete Mathematics
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The notion of exponential Dowling structures is introduced, generalizing Stanley's original theory of exponential structures. Enumerative theory is developed to determine the Mobius function of exponential Dowling structures, including a restriction of these structures to elements whose types satisfy a semigroup condition. Stanley's study of permutations associated with exponential structures leads to a similar vein of study for exponential Dowling structures. In particular, for the extended r-divisible partition lattice we show that the Mobius function is, up to a sign, the number of permutations in the symmetric group on rn+k elements having descent set {r,2r,...,nr}. Using Wachs' original EL-labeling of the r-divisible partition lattice, the extended r-divisible partition lattice is shown to be EL-shellable.