Hamilton Bailey, 1 October 1894

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...

Lecture 8: October 1

Consider a simply connected region S of the two-dimensional Cartesian lattice (e.g. a 2n× 2n chessboard). A tiling of S is a covering of all its squares by non-overlapping dominoes, each of which occupies two adjacent squares of the lattice. We want to generate u.a.r. a tiling of S. Such problems arise in statistical physics, where the tilings correspond to configurations of a so-called dimer s...

Cover Special (1) Issue vol. 15, no. 7, October 2018

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.

October 2002 Proton Decay 1

We discuss the status of supersymmetric grand unified theories [SUSY GUTs] with regards to the observation of proton decay. In this talk we focus on SUSY GUTs in 4 dimensions. We outline the major theoretical uncertainties present in the calculation of the proton lifetime and then present our best estimate of an absolute upper bound on the predicted proton lifetime. Towards the end, we consider...