Michiel Hazewinkel

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In this lecture I discuss some aspects of MKM, Mathematical Knowledge Management, with particuar emphasis on information storage and information retrieval. 1. Is there a problem? The issue at hand is that of information storage and information retrieval as regards mathematics. Or, concentrating on the latter, if one has a mathematical question, can one find(More)
Let A be a bipartite graph between two sets D and T. Then A defines by Hamming distance, metrics on both T and D. The question is studied which pairs of metric spaces can arise this way. If both spaces are trivial the matrix A comes from a Hadamard matrix or is a BIBD. The second question studied is in what ways A can be used to transfer (classification)(More)
Let A be a reduced incidence relation between n lines and m points. Suppose that (a) Through each two points there pass λ lines (b) Each two lines intersect in µ points. If λ µ = = 1 assume, moreover, that there are four points no three of which are on one line. Then n m = , λ µ = , and there is a number r such that all lines have r points and through each(More)
Let Z denote the free associative algebra ZhZ1; Z2 ; : : :i over the integers. This algebra carries a Hopf algebra structure for which the comultiplication is Zn 7 ! i+j=nZi Zj. This the noncommutative Leibniz-Hopf algebra. It carries a natural grading for which gr(Zn) = n. The Ditters-Scholtens theorem says that the graded dual, M, of Z, herein called the(More)