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DTSTAMP:20210331T200000Z
UID:1616767751211@events.msu.edu
CATEGORIES:Conferences / Seminars / Lectures
DTSTART:20210331T200000Z
DTEND:20210331T205000Z
SUMMARY:Math Seminar Series
DESCRIPTION:
 Combinatorics and Graph Theory\n
 \n
 Ira Gessel, 
 Brandeis University, will be speaking.\n
 \n
 The 
 topic is "Counting graphs with neighborhood 
 restrictions."\n
 \n
 Contact Bruce E Sagan (bsagan@msu.edu) 
 for more information.\n
 \n
 A graph 
 is called point-determining (or mating type) 
 if no two vertices have the same neighborhood. 
 An arbitrary graph can be reduced to a point-determining 
 graph by contracting each set of 
 vertices with the same neighborhood to a single 
 vertex, and this decomposition enables us 
 to give a simple exponential generating function 
 for counting point-determining graphs, 
 as accomplished by Ronald Read in 1989. In this 
 talk we will discuss a closely related problem: 
 counting graphs in which no two vertices 
 have complementary neighborhoods. The decomposition 
 approach does not work here. Instead 
 we apply inclusion-exclusion, similarly to its 
 use in rook theory, to obtain a simple exponential 
 generating function for these graphs. 
 We also discuss how this application of inclusion-exclusion 
 is related to Möbius inversion, 
 and how it can be applied to some related 
 problems.\n\n
 Price: free\n
 Sponsor: Department of Mathematics\n
 Sponsor's Homepage: https://www.math.msu.edu/\n
 Contact name: Department of Mathematics\n
 Contact phone: (517) 353-0844\n
 for more info visit the web at:\n 
 https://www.math.msu.edu/Seminars/CalendarView.aspx?month-of=September2016\n
LOCATION:Online via Zoom
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