Kessler and Livingstone proved an asymptotic formula for the expected length of the largest part of a partition drawn uniformly at random. As a first step they gave an exact formula expressed as a weighted sum of Euler’s partition function. Here we give a short bijective proof of a generalization of this exact formula to the expected length of the kth part. 1. Results By λ ! n we will mean that...

We introduce a new spectral sequence called the p-chain spectral sequence which converges to the (co-)homology of a contravariant C-space with coefficients in a covariant C-spectrum for a small category C. It is different from the corresponding Atiyah–Hirzebruch-type spectral sequence. It can be used in combination with the Isomorphism Conjectures of Baum and Connes and Farrell and Jones to com...

Abstract. It is well known from a result by Shapiro-Shields that in the Hardy spaces, a sequence of reproducing kernels is uniformly minimal if and only if it is an unconditional basis in its span. This property which can be reformulated in terms of interpolation and so-called weak interpolation is not true in Paley-Wiener spaces in general. Here we show that the Carleson condition on a sequenc...

Abstract. Let α, β, and γ be partitions describing the isomorphism types of the finite abelian p-groups A, B, and C. From theorems by Green and Klein it is well-known that there is a short exact sequence 0→ A→ B → C → 0 of abelian groups if and only if there is a Littlewood-Richardson sequence of type (α, β, γ). Starting from the observation that a sequence of partitions has the LR property if ...

BCK-modules were introduced as an action of a BCK-algebra over Abelian group. Homomorphisms form exact sequence which is called BCK-sequence. In this paper, we study homomorphisms BCK-modules. We show that have module structure. Moreover, sequences Hom functors are BCK-sequences.

The amino acid sequences corresponding to the vacA intermediate region from 39 isolates of Helicobacter pylori were investigated. The substitution of a G for the third S in the i1-type cluster B sequence (QASEGITSSK) conferred a greater risk of gastric diseases (P < 0.03; Fisher's exact test). The conserved substitutions of an F for the Y in the cluster A sequence and of an M for the second N i...