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SUMMARY:Counting graphic sequences - Paul Balister (Oxford)
DTSTART:20230518T130000Z
DTEND:20230518T140000Z
UID:TALK201229@talks.cam.ac.uk
CONTACT:HoD Secretary\, DPMMS
DESCRIPTION:Given an integer $n$\, let $G(n)$ be the number of integer seq
 uences\n$n−1≥d_1≥d_2≥⋯≥d_n≥0$ that are the degree sequence o
 f some graph. We show that\n$G(n)=(c+o(1))4^n/n^{3/4}$ for some constant $
 c>0$\, improving both the previously\nbest upper and lower bounds by a fac
 tor of $n^{1/4+o(1)}$. The proof relies on a\ntranslation of the problem i
 nto one concerning integrated random walks.\n\nJoint work with Serte Donde
 rwinkel\, Carla Groenland\, Tom Johnston and Alex Scott.
LOCATION:MR12
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