We investigate Γ-cohomology of some commutative cooperation algebras E∗E associated with certain periodic cohomology theories. For KU and E(1), the Adams summand at a prime p, and for KO we show that Γ-cohomology vanishes above degree 1. As these cohomology groups are the obstruction groups in the obstruction theory developed by Alan Robinson we deduce that these spectra admit unique E∞ structu...

We refine our earlier work on the existence and uniqueness of E∞ structures on K-theoretic spectra to show that at each prime p, the connective Adams summand ℓ has an essentially unique structure as a commutative S-algebra. For the p-completion ℓp we show that the McClure-Staffeldt model for ℓp is equivalent as an E∞ ring spectrum to the connective cover of the periodic Adams summand Lp. We est...

In this paper we study the modular structure of the permutation module H ) of the symmetric group S2n acting on set partitions of a set of size 2n into n sets each of size 2, defined over a field of odd characteristic p. In particular we characterize the vertices of the indecomposable summands of H ) and fully describe all of its indecomposable summands that lie in blocks of p-weight at most tw...

We define holomorphic connection on a parabolic vector bundle over a Riemann surface and prove that a parabolic vector bundle admits a holomorphic connection if and only if each direct summand of it is of parabolic degree zero. This is a generalization to the parabolic context of a well-known result of Weil which says that a holomorphic vector bundle on a Riemann surface admits a holomorphic co...

We present telescoping algorithms which compute optimal sum representations of indefinite nested sums. More precisely, given a rational summand expression in terms of nested sums and products, the algorithm splits the summand into a summable part, which can be summed by telescoping, and into a non-summable part, which is degree-optimal with respect to one of the most nested sums or products. If...

A composition of a positive integer n consists of an ordered sequence of positive integers whose sum is n. We investigate compositions in which the summand 2 is not allowed, and count the total number of such compositions and the number of occurrences of the summand i in all such compositions. Furthermore, we explore patterns in the values for Cj(n, 2̂), the number of compositions of n without 2...

1. INTRODUCTION. In his 1974 book entitled " The Life and Times of the Central Limit Theorem, " Adams [1] describes this theorem as " one of the most remarkable results in all of mathematics " and " a dominating personality in the world of probability and statistics. " More than three decades later, his description is not only still pertinent but has also been corroborated and reinforced by dev...

In this paper we provide a simple characterization of the dominance in two classes of continuous triangular norms. In particular, we solve the dominance of (i) ordinal sum t-norms that use the Łukasiewicz t-norm as the only summand operation and (ii) ordinal sum t-norms that use the product t-norm as the only summand operation. In both cases, the dominance relation is characterized by a simple ...