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DTSTART;TZID=America/Los_Angeles:20190423T121500
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DTSTAMP:20260423T114941
CREATED:20190312T201357Z
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UID:1273-1556021700-1556025000@colleges.claremont.edu
SUMMARY:Theory of vertex Ho-Lee-Schur graphs (Sin-Min Lee\, SJSU)
DESCRIPTION:A triple of natural numbers (a\,b\,c) is an S-set if a+b=c. I. Schur used the S-sets to show that for n >3\, there exists s(n) such that for prime p > s(n)\, x^p + y^p = z^p (mod p) has a nontrivial solution. A (p\,q)-graph G is said to be vertex Ho-Lee-Schur graph if there exists a bijection f: V(G) –> {1\,2\,…\,p} such that for each C3 subgraph of G with vertices {x\,y\,z} the triple (f(x)\,f(y)\,f(z)) is an S-set. The VHLS deficiency of G is the smallest k such that GU Nk\, where Nk is null graph\,  is a vertex Ho-Lee-Schur graph. We determine VHLS deficiency of some graphs and show that no Kuratowski type characterization of non-vertex Ho-Lee-Schur graphs. Some relation of integer partitions and this theory  is explored. We will also introduce some unsolved problems and invite the audience to  solve them.
URL:https://colleges.claremont.edu/ccms/event/theory-of-vertex-ho-lee-schur-graphs-sin-min-lee-sjsu/
LOCATION:Millikan 2099\, Pomona College\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
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