We give a formula for a morphism between Specht modules over (Z/m)Sn, where n ≥ 1, and where the partition indexing the target Specht module arises from that indexing the source Specht module by a downwards shift of one box, m being the box shift length. Our morphism can be reinterpreted integrally as an extension of order m of the corresponding Specht lattices.

We give several equivalent combinatorial descriptions of the space of states for the box-ball systems, and connect certain partition functions for these models with the q-weight multiplicities of the tensor product of the fundamental representations of the Lie algebra gl(n). As an application, we give an elementary proof of the special case t = 1 of the Haglund–Haiman–Loehr formula. Also, we pr...

ions and first-class procedures We've seen two ways to express the square-root computation as an instance of a more general method, once as a fixed-point search and once using Newton's method. Since Newton's method was itself expressed as a fixed-point process, we actually saw two ways to compute square roots as fixed points. Each method begins with a function and finds a fixed point of some tr...

Growth in an adjacent market is tougher than it looks; three-quarters of the time, the effort fails. But companies can change those odds dramatically. Results from a five-year study of corporate growth conducted by Bain & Company reveal that adjacency expansion succeeds only when built around strong core businesses that have the potential to become market leaders. And the best place to look for...

Twenty five years after the original epidemiological studies 2 two thirds of all patients with coronary artery disease still die before reaching hospital (p 1065). These patients have no opportunity to benefit from the advances in hospital treatment of acute myocardial infarction, such as thrombolysis, that have dramatically reduced mortality in hospital. It is particularly sobering to see in t...