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DTSTART;TZID=America/Toronto:20230619T113000
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URL:https://uwaterloo.ca/combinatorics-and-optimization/events/algebraic-gr
 aph-theory-sung-song
SUMMARY:Algebraic Graph Theory - Sung Song
CLASS:PUBLIC
DESCRIPTION:TITLE: Partial geometric designs\, directed strongly regular gr
 aphs\,\nand association scheme\n\nSPEAKER:\n Sung Song\n\nAFFILIATION:\n I
 owa State University\n\nLOCATION:\n Please contact Sabrina Lato for Zoom
  link\n\nABSTRACT: A partial geometric design with parameters $(v\, b\, k\
 , r\;\n\\alpha\, \\beta)$ is a tactical configuration $(P\, \\mathcal{B})$
  (with\n$|P|=v$\, $|\\mathcal{B}|=b$\, every point $p\\in P$ belonging to 
 $r$\nblocks\, and every block $B\\in\\mathcal{B}$ consisting of $k$ points
 )\nsatisfying the property: \n\n{for any pair $(p\, B)\\in P\\times \\math
 cal{B}$\, the number of flags\n$(q\, C)$ with $q\\in B$ and $C\\ni p$ equa
 ls to $\\alpha  \\mbox{ if }\np\\notin B$ and to $\\beta  \\mbox{ if } p
 \\in B$.}\n\nNeumaier studied partial geometric designs in detail in his a
 rticle\,\n``$t\\frac12$-designs\,\" [JCT A {\\bf 28}\, 226-248 (1980)]. He
 \ninvestigated their connection with strongly-regular graphs and gave\nvar
 ious characterizations of partial geometries\, bipartite graphs\,\nsymmetr
 ic 2-designs\, and transversal designs in terms of partial\ngeometric desi
 gns.
DTSTAMP:20260403T014420Z
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