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Activity Number: 371
Type: Contributed
Date/Time: Tuesday, August 6, 2013 : 10:30 AM to 12:20 PM
Sponsor: IMS
Abstract - #309229
Title: Some Comments on Anderson Graphs for Classic Order-4 Magic Squares
Author(s): George Styan*+
Companies: McGill University Dept of Mathematics & Statistics
Keywords: contingency tables ; classification ; magic squares ; matrix factorizations ; Anderson graphs ; Dudeney types
Abstract:

We present several new classifications and corresponding contingency tables for the 880 classic order-4 magic squares first enumerated by the French mathematician Bernard Frenicle de Bessy (c.~1605-1675). We identify 382 distinct Anderson graphs (Bragdon's ``magic lines'' diagrams, Moran's ``sequence designs'') and study their symmetry and path lengths, building on results by Francis James Anderson (1860-1920), Claude Fayette Bragdon (1866-1946), and James Sterling Moran (1908-1999). Our ``Anderson graph'' is the graph produced by the lines joining the consecutive numbers in the magic square in sequence. We also consider matrix factorizations due to the mathematicians Leonhard Euler (1707-1783) and Friedrich Fitting (1862-1945), and classifications due to Frenicle and to mathematical puzzle aficionado Henry Ernest Dudeney (1857-1930). We illustrate our findings as much as possible and whenever feasible with images of postage stamps or other philatelic items. This is joint research wth Reijo Sund (Helsinki) and Walter Trump (Nurnberg). With this talk we are pleased to celebrate the International Year of Statistics 2013 and the special year for Mathematics of Planet Earth 2013.


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