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SUMMARY:Lindsay Dever (Millersville University)
DTSTART:20260717T203000Z
DTEND:20260717T205500Z
DTSTAMP:20260710T111541Z
UID:CANT2026/74
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2026/74/
 ">Atoms in the semigroup of non-negative integer matrices</a>\nby Lindsay 
 Dever (Millersville University) as part of Combinatorial and additive numb
 er theory seminar (CANT 2026)\n\nLecture held in Science Center in the CUN
 Y Graduate Center (4th floor).\n\nAbstract\nIn the semigroup of $2\\times 
 2$ matrices with non-negative integer entries and non-zero determinant\, w
 e study the factorization of matrices into atoms\, or irreducible matrices
 . In 2022\, Baeth et al. discovered classes of atoms in this semigroup\; h
 owever\, the factorability of most matrices remains unknown. As the result
  of joint work with Eva Goedhart\, Gregory Heilbrunn\, and Tony W. H. Wong
 \, I will discuss additional classes of atoms: a class of atoms with deter
 minant $p$\, $2p$\, or $4p$\, where $p$ is prime\, and a class of atoms wh
 ere the main diagonal is much ``larger'' than the off-diagonal (or vice-ve
 rsa). In addition\, we find that bisymmetric matrices with relatively prim
 e entries are a divisor-closed subset and use a factor-search algorithm to
  classify bisymmetric atoms with minimum entry up to 4000.\n
LOCATION:https://researchseminars.org/talk/CANT2026/74/
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