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DTSTART:20240310T070000
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DTSTART:20231105T060000
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DTSTART;TZID=America/Toronto:20240604T100000
SEQUENCE:0
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URL:https://uwaterloo.ca/pure-mathematics/events/number-theory-seminar-121
SUMMARY:Number Theory Seminar
CLASS:PUBLIC
DESCRIPTION:Speaker: Gauree Wathodkar\, University of Mississippi\n\n_\"Pa
 rtition regularity in commutative rings.\"_\n\nLet A ∈ Mm×n(Z) be a mat
 rix with integer coefficients. The system\nof equations A⃗x = ⃗0 is sa
 id to be partition regular over Z if\nfor every finite partition Z \\ {0} 
 = ∪ri =1Ci\, there exists a\nsolution ⃗x ∈ Zn\, all of whose compone
 nts belonging to the same\nCi. For example\, the equation x + y − z = 0 
 is partition regular. In\n1933 Rado characterized completely all partition
  regular matrices. He\nalso conjectured that for any partition Z \\ {0} = 
 ∪ri =1Ci\, there\nexists a partition class Ci that contains solutions to
  all partition\nregular systems. This conjecture was settled in 1975 by De
 uber. We\nstudy the analogue of Rado’s conjecture in commutative rings\,
  and\nprove that the same conclusion holds true in any integral domain.\n\
 nMC5403
DTSTAMP:20260512T220424Z
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