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BEGIN:VEVENT
UID:3b0d4860c0858b84f2d8a6312d0c1668
CATEGORIES:Experimental Mathematics Seminar
CREATED:20201201T104117
SUMMARY:Counting Matrices that are Squares
LOCATION:zoom
DESCRIPTION:Abstract: On the math-fun mailing list (7 May 2013), Neil Sloane asked to c
 alculate the number of n times n matrices with entries in {0,1} which are s
 quares of other such matrices. In this paper we analyze the case that the a
 rithmetic is in GF(2) We follow the dictum of Wilf (in the paper ``What is 
 an answer?'') to derive a ``effective'' algorithm to count such matrices in
  much less time than it takes to enumerate them. The algorithm which we use
  involves the analysis of conjugacy classes of matrices. The restricted int
 eger partitions which arise are counted by the coefficients of one of Raman
 ujan's mock Theta functions, which we found thanks to Sloane's OEIS (Online
  Encyclopedia of Integer Sequences).\n
X-ALT-DESC;FMTTYPE=text/html:<p><i><em style="text-align: left; color: #000000; text-transform: none; te
 xt-indent: 0px; letter-spacing: normal; font-family: Times New Roman; font-
 size: 16px; font-variant: normal; font-weight: 400; text-decoration: none; 
 word-spacing: 0px; white-space: normal; orphans: 2;">Abstract</em></i>: On 
 the math-fun mailing list (7 May 2013), Neil Sloane asked to calculate the 
 number of n times n matrices with entries in {0,1} which are squares of oth
 er such matrices. In this paper we analyze the case that the arithmetic is 
 in GF(2) We follow the dictum of Wilf (in the paper ``What is an answer?'')
  to derive a ``effective'' algorithm to count such matrices in much less ti
 me than it takes to enumerate them. The algorithm which we use involves the
  analysis of conjugacy classes of matrices. The restricted integer partitio
 ns which arise are counted by the coefficients of one of Ramanujan's mock T
 heta functions, which we found thanks to Sloane's OEIS (Online Encyclopedia
  of Integer Sequences).</p>
CONTACT:Victor S. Miller, Center for Communications Research, Princeton. 
X-EXTRAINFO:Zoom link: https://rutgers.zoom.us/j/94346444480 \npassword: 6564120420 
DTSTAMP:20260828T110908
DTSTART;TZID=America/New_York:20210128T170000
DTEND;TZID=America/New_York:20210128T180000
SEQUENCE:0
TRANSP:OPAQUE
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