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DTSTART:20250309T070000
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DTSTART;TZID=America/Toronto:20250602T113000
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URL:https://uwaterloo.ca/combinatorics-and-optimization/events/algebraic-gr
 aph-theory-amin-bahmanian
SUMMARY:Algebraic Graph Theory-Amin Bahmanian
CLASS:PUBLIC
DESCRIPTION:TITLE: A Sudoku Baranyai's Theorem\n\nSPEAKER:\n Amin Bahmania
 n\n\nAFFILIATION: \n\nIllinois State University \n\nLOCATION:\n Please co
 ntact Sabrina Lato for Zoom link.\n\nABSTRACT: Motivated by constructing
  higher dimensional Sudokus we\ngeneralize the famous Baranyai's theorem. 
 Let$n=\\prod_{i=1}^d a_i$.\nSuppose that an $n\\times\\dots \\times n$ ($d
 $ times) array $L$ is\npartitioned into$n/a_1\\times\\dots\\times n/a_d$ s
 ub‐arrays (called\nblocks). Can we color the $n^d$ cells of $L$ with $n^
 {d21}$ colors so\nthat each layer (obtained by fixing one coordinate) and 
 each\n$n/a_1\\times\\dots\\times n/a_d$block contains each color exactly o
 nce?\nWe generalize the well‐know theorem of Baranyai to answer this\nqu
 eestion. The case $d=2 a_1=a_2=3$ corresponds to the usual Sudoku.\nWe als
 o provide finite fieldconstruction of various related objects.\nThis is jo
 int work with Sho Suda.
DTSTAMP:20260403T081758Z
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