Statistics.William B. Bailey , John Cummings

Lifting Bailey pairs to WP-Bailey pairs

A pair of sequences (αn(a, k, q),βn(a, k, q)) such that α0(a, k, q) = 1 and βn(a, k, q) = n ∑ j=0 (k/a; q)n−j(k; q)n+j (q; q)n−j(aq; q)n+j αj(a, k, q) is termed a WP-Bailey Pair. Upon setting k = 0 in such a pair we obtain a Bailey pair. In the present paper we consider the problem of “lifting” a Bailey pair to a WPBailey pair, and use some of the new WP-Bailey pairs found in this way to derive...

Shifted versions of the Bailey and well-poised Bailey lemmas

The Bailey lemma is a famous tool to prove Rogers-Ramanujan type identities. We use shifted versions of the Bailey lemma to derive mversions of multisum Rogers-Ramanujan type identities. We also apply this method to the Well-Poised Bailey lemma and obtain a new extension of the Rogers-Ramanujan identities.

The Clinics of John B. Murphy

The Clinics of John B. Murphy, M.D.

Jay Cummings: Research Statement

My research has touched many areas of combinatorics, including enumerative, algebraic, spectral, extremal and probabilistic. The projects below include finding the stationary distribution of a random coloring procedure, pursuing new directions in the math of juggling, working with undergraduates on Ramsey theory, and studying a pair of topics from spectral graph theory. I have mentored undergra...