Exponential Dowling structures

The notion of exponential Dowling structures is introduced, generalizing Stanley's original theory of exponential structures. Enumerative theory is developed to determine the M\"obius 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 the M\"obius 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.Comment: 17 page

Shellability of generalized Dowling posets

A generalization of Dowling lattices was recently introduced by Bibby and Gadish, in a work on orbit configuration spaces. The authors left open the question as to whether these posets are shellable. In this paper we prove EL-shellability and use it to determine the homotopy type. We also show that subposets corresponding to invariant subarrangements are not shellable in general

Managing A Digitization Project: One Library\u27s Experience

The Jessie C. Eury Library of Lincoln Christian College and Seminary (Lincoln, IL) is proud of the Hymnals of the Stone-Campbell Movement: Enos E. Dowling Hymnal Collection on its website at www.lccs.edu/library/hymnals. This online collection of more than 9,000 hymns from rare 19th century hymnals features works by Alexander Campbell, J.T. Johnson, Walter Scott, and Illinois residents such as Barton W. Stone, Silas W. Leonard, and the Fillmore Brothers. These hymnals were selected from some 2,000 gathered by Mr. Dowling, former academic dean at Lincoln Christian Seminary, throughout his lifetime, including nearly 200 affiliated with the Restoration Movement that arose from the 19th century Stone-Campbell religious heritage on the American frontier. His collection is one of the largest-known compilations of hymnals representing this religious movement and serves to illustrate changing religious musical styles

Recurrence Relations for Strongly q-Log-Convex Polynomials

We consider a class of strongly q-log-convex polynomials based on a triangular recurrence relation with linear coefficients, and we show that the Bell polynomials, the Bessel polynomials, the Ramanujan polynomials and the Dowling polynomials are strongly q-log-convex. We also prove that the Bessel transformation preserves log-convexity.Comment: 15 page