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BEGIN:VEVENT
UID:6e82beb4f4b3c6ab2a0bd12ba85c104a
CATEGORIES:Discrete Math
CREATED:20230306T125229
SUMMARY:Enumerating interval graphs and d-representable complexes
LOCATION:Hill Center Room 705
DESCRIPTION:Abstract: How many different ways can we arrange n convex sets in R^d? One 
 answer is provided by counting the number of d-representable complexes on v
 ertex set [n]. We show that there are exp(Theta(n^d log n)) many such compl
 exes, and provide bounds on the constants involved. As a consequence, we sh
 ow that d-representable complexes comprise a vanishingly small fraction of 
 d-collapsible complexes. In the case d=1 our results are more precise, and 
 improve the previous best estimate for the number of interval graphs. These
  results are joint work with Boris Bukh.\n
X-ALT-DESC;FMTTYPE=text/html:<p><strong>Abstract</strong>: How many different ways can we arrange n conv
 ex sets in R^d? One answer is provided by counting the number of d-represen
 table complexes on vertex set [n]. We show that there are exp(Theta(n^d log
  n)) many such complexes, and provide bounds on the constants involved. As 
 a consequence, we show that d-representable complexes comprise a vanishingl
 y small fraction of d-collapsible complexes. In the case d=1 our results ar
 e more precise, and improve the previous best estimate for the number of in
 terval graphs. These results are joint work with Boris Bukh.</p>
CONTACT: Amzi Jeffs (Carnegie Mellon)
DTSTAMP:20260827T094946
DTSTART;TZID=America/New_York:20230306T140000
DTEND;TZID=America/New_York:20230306T150000
SEQUENCE:0
TRANSP:OPAQUE
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