Albert Nijenhuis

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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)
The Frobenius problem, also known as the postage-stamp problem or the money-changing problem, is an integer programming problem that seeks nonnegative integer solutions to x 1 a 1 + · · · + x n a n = M , where a i and M are positive integers. In particular, the Frobenius number f (A), where A = {a i }, is the largest M so that this equation fails to have a(More)
We investigated the peroxisomal fatty acid beta-oxidation system in liver and cultured skin fibroblasts from patients with X-linked adrenoleukodystrophy known to accumulate very long chain fatty acids. In order to examine whether the deficient peroxisomal oxidation of very long chain fatty acids in these patients results from a deficiency in one of the(More)
Profiles of saturated very-long-chain (> C22) fatty acids were studied in plasma, fibroblasts, erythrocytes, platelets, and leukocytes of patients affected by peroxisomal disorders such as Zellweger syndrome, X-linked adrenoleukodystrophy (X-ALD), and classic rhizomelic chondrodysplasia punctata (RCDP) and in controls. In Zellweger patients, the(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 the number of partitions of n whose parts all lie in a fixed finite set T of positive integers. We find the(More)