Some construction methods of the variance balanced block designs with repeated blocks are given. They are based on the incidence matrices of the balanced incomplete block designs with repeated blocks.

The first part of these lectures introduces the Smith normal form and the invariant factors of an integer matrix, and the relation of Smith form to systems of linear diophantine equations. We give selected examples of how invariant factors appear and may be applied to the theory of combinatorial designs. Importantly, we may sometimes construct sefl-dual p-ary codes from hypothetical designs and...

Let P i n be the poset of partitions of an integer n, ordered by re-nement. Let b(P i n) be the largest size of a level and d(P i n) be the largest size of an antichain of P i n. We prove that d(P i n) b(P i n) e + o(1) as n ! 1: The denominator is determined asymptotically. In addition, we show that the incidence matrices in the lower half of P i n have full rank, and we prove a tight upper bo...

This paper examines the utility gains and losses induced by changes in capital taxation in an economy with heterogeneous discount factors. A Ramsey equilibrium, where households earn wage income and accumulate capital, but may not borrow against future wage income, provides a natural setting for this analysis. In the short run, the agents with little or no capital gain from increased transfers ...

We present a method to construct new tilting complexes from existing ones using tensor products, generalizing a result of Rickard. The endomorphism rings of these complexes are generalized matrix rings that are “componentwise” tensor products, allowing us to obtain many derived equivalences that have not been observed by using previous techniques. Particular examples include algebras generalizi...

The dimensions of the codes associated to the Ree unital are computed using methods from modular representation theory.

The notion of reduced incidence algebra of an arbitrary cobweb poset is delivered.

The nnnrlnip of inclusion and exclusion and Consecutive Sets M. H. McIlwain )p'n,Clrj·'Yli'·nl of Mathematics Furman University Greenville, SC USA 29613 applied to numerous areas of discrete and combinatorial mathematics. One manifestation of this occurs in probability of the union of events an alternating sum of pn)o(HHjlIW~S of various intersections of events. If the constituent events are th...