Albert Nijenhuis

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Introduction. In an address to the Society in 1962, one of the authors gave an outline of the similarities between the deformations of complex-analytic structures on compact manifolds on one hand, and the deformations of associative algebras on the other. The first theory had been stimulated in 1957 by a paper [7] by NijenhuisFrölicher and extensively(More)
Combinatorial properties of vector spaces over finite fields have been extensively investigated (see Goldman and Rota [ 1, 21, Knuth [3], Milne [4], Calabi and Wilf [S], etc.). In this paper we will obtain a number of results by a unified method. The method, as used in [5], is the observation that the canonical invariant of a vector subspace over a finite(More)
Let Sz be the set of positive integers that are omitted values of the form f = z”= a.x. where the a, are fixed and relatively prime natural numbers *1 $1) and the xi are variable nonnegative integers. Set w = #Q and K = max 0 + 1 (the conductor). Properties of w and K are studied, such as an estimate for w (similar to one found by Brauer) and the inequality(More)
The Frobenius problem, also known as the postage-stamp problem or the moneychanging problem, is an integer programming problem that seeks nonnegative integer solutions to x1a1 + · · · + xnan = M , where ai and M are positive integers. In particular, the Frobenius number f(A), where A = {ai}, is the largest M so that this equation fails to have a solution. A(More)
If p(n, k) is the number of partitions of n into parts <k. then the sequence { p(k, li), p(k + 1, Ii)....} is periodic modulo a prime p. We find the minimum period Q = Q(li, p) of this sequence. More generally, we find the minimum period, modulo P, of {pW Vi,,,. the number of partitions of n whose parts all lie in a fixed finite set T of positive integers.(More)
This paper contains a short proof of a formula by Frame, Robinson, and Thrall [I] h h w ic counts the number of Young tableaux of a given shape. Let X = {X, >, X, > ..’ 2 X,} be a partition of R. The Ferrers diagram of h is an array of cells doubly indexed by pairs (i, j) with 1 < i < m, 1 <j < A( . A Young tableau of shape h (sometimes called a standard(More)
The purpose of this note is to announce several results on deformations of homomorphisms of Lie groups and Lie algebras. Our main theorems are precise analogues of two basic theorems on deformations of complex analytic structures on compact manifolds, the rigidity theorem of Frölicher-Nijenhuis [3] and the local completeness theorem of Kuranishi fs]. In our(More)
Inoculation of 3 x 10(4) to 3 x 10(5) CC531 colon adenocarcinoma cells into the portal vein of syngeneic WAG/Rij rats provides a reproducible animal model of colon cancer liver metastasis with macroscopically visible tumor nodules at day 25 after inoculation. In this study, the inflammatory cell response in the liver sinusoids against locally induced(More)
In this note we describe a general principle for selecting at random from a collection of combinatorial objects, where “at random” means in such a way that each of the objects has equal probability, a priori, of being selected. We apply this principle by displaying two algorithms, the first of which will select a random partition of an integer n, and the(More)