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SUMMARY:Professor RICHARD BRUALDI (University of Wisconsin\, USA)
DTSTART:20211217T010000Z
DTEND:20211217T023000Z
DTSTAMP:20260423T005832Z
UID:ITB-MDLS/4
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/ITB-MDLS/4/"
 >Permutation Matrices\, Alternating Sign Matrices\, and Generalizations</a
 >\nby Professor RICHARD BRUALDI (University of Wisconsin\, USA) as part of
  ITB Mathematics Distinguished Lecture Series\n\n\nAbstract\nThe study of 
 permutations is both ancient and modern. One can view them as the integers
  1\,2\, … \, n in some order or as n x n permutation matrices.  They can
  be regarded as data which is to be sorted. The explicit definition of the
  determinant uses permutations.  An inversion of a permutation occurs when
  a larger integer precedes a smaller integer. Inversions can be used to de
 fine two partial orders on permutations\, one weaker than the other. Parti
 al orders have a unique minimal completion to a lattice\, the Dedekind-Mac
 Neille completion. Generalizations of permutation matrices determine relat
 ed matrix classes\, for instance\, alternating sign matrices (ASMs) which 
 arose independently in the mathematics and physics literature. Permutation
 s may contain certain patterns\, e.g. three integers in increasing order\;
  avoiding such patterns determines certain permutation classes. Similar re
 strictions can be placed more generally on (0\,1)-matrices. \n\nThere are 
 continuous analogs of permutation matrices and alternating sign matrices\,
  and even higher dimension analogs. We shall explore these and other ideas
  and their connections.\n
LOCATION:https://researchseminars.org/talk/ITB-MDLS/4/
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