Eğecioğlu and Remmel [2] gave an interpretation for the entries of the inverse Kostka matrix K in terms of special rim-hook tableaux. They were able to use this interpretation to give a combinatorial proof that KK = I but were unable to do the same for the equation KK = I. We define an algorithmic signreversing involution on rooted special rim-hook tableaux which can be used to prove that the l...

land, and Sir Arthur Stanley is, if anything, unduly modest when he says that its figures " prove that the voluntary system is holding its own." It is, indeed} doing much more than that. Not only did the combined income of these 705 hospitals reach the splendid total of ?7,689,000, but it showed a surplus of ?213,000 of ordinary income over ordinary expenditure. The improvement, as compared wit...

It is shown that there is an absolute positive constant δ > 0, so that for all positive integers k and d, there are sets of at least d log2(k+2)/ log2 log2(k+2) nonzero vectors in R, in which any k+ 1 members contain an orthogonal pair. This settles a problem of Füredi and Stanley.

Not only the general theme of madness, but also features narrative allow us to compare Garshin’s "A Red Flower" with "The Dream a Ridiculous Man" by Dostoevsky and "Ward No. 6" Chekhov. It turns out that storytelling process creates similar problems, solution which each writer provides in his own way: see personalisation, dual apparent objec...

We give an account of our work on transitive factorizations of permutations. The work has had impact upon other areas of mathematics such as the enumeration of graph embeddings, random matrices, branched covers, and the moduli spaces of curves. Aspects of these seemingly unrelated areas are seen to be related in a unifying view from the perspective of algebraic combinatorics. At several points ...