A strong complete mapping of a group G is a bijection θ : G → G for which both mappings x 7→ xθ(x) and x 7→ x−1θ(x) are bijections. We characterize finite abelian groups that admit strong complete mappings, thus solving a problem posed by Horton in 1990. We also prove the existence of strong complete mappings for countably infinite groups.

We consider the Horton-Strahler number S, for random equiprobable binary trees with n nodes. We give a simple probabilistic proof of the well-known result that ES, = log,n + O(1) and show that for every x > 0, P{ 1 S, log,n ( > x} Q D/4x, for some constant D > 0.

La maladie de Horton est une vascularite segmentaire et focale qui touche les artères de gros et moyen calibre, intéressant préférentiellement les branches de l'artère carotide externe. L'atteinte aortique est observée dans 5 à 15 % des cas, mais elle est probablement sous-estimée en raison d'une symptomatologie souvent pauvre ou peu spécifique. Elle est rarement inaugurale et survient le plus ...

Kazushi Imai, Seema S. Dalal, John Hambor, Peter Mitchell, Yasunori Okada, William C. Horton, and Jeanine D’Armiento Division of Molecular Medicine, Department of Medicine, College of Physicians and Surgeons of Columbia University, New York, New York; Central Research Division, Pfizer Inc., Groton, Connecticut; Department of Pathology, School of Medicine, Keio University, Tokyo, Japan; and Emor...

By T. H. J. HUISMAN, A. M. Dozy, B. E. HORTON AND J. B. WILsON T HE EXISTENCE of variants of normal human fetal hemoglobin ( HbFor a2y2 ) has been suggested in different reports in the literature. Variants of fetal hemoglobin with abnormal a-polypeptide chains have been described5 ”5 and some are well characterized.’0 Only one abnormality, namely the electrophoretically fast moving hemoglobin v...