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DESCRIPTION: We say that a sequence {π _ i  } of permutations is quasirando
 m if\, for each k&gt\;1 and each σ∈ S  _ k  \, the probability that a unifo
 rmly chosen  k-set of entries of π  _ i   induces σ tends to 1/ k ! as  i  
 tends to infinity. It is known that a much weaker condition already forces 
 π _ i   to be quasirandom\; namely\, if the above property holds for all σ∈
  S  4 . We further weaken this condition by exhibiting sets S⊆ S  4 \, such
  that if randomly chosen four entries of π _ i   induce an element of  S  w
 ith probability tending to | S |/24\, then {π _ i  } is quasirandom. Moreov
 er\, we are able to completely characterise the sets  S  with this property
 . In particular\, there are exactly ten such sets\, the smallest of which h
 as cardinality eight. This is joint work with Timothy Chan\, Daniel Král'\,
  Jon Noel\, Maryam Sharifzadeh and Jan Volec. 
DTSTAMP:20200122T165400
DTSTART:20200203T160000
CLASS:PUBLIC
LOCATION:Freie Universität Berlin \n Institut für Informatik \n Takustr. 9 
 \n 14195 Berlin \n Room 005 (Ground Floor)
SEQUENCE:0
SUMMARY:Yanitsa Pehova (University of Warwick): Characterisation of quasira
 ndom permutations by a pattern sum
UID:104961400@/www.mi.fu-berlin.de
URL:https://www.mi.fu-berlin.de/en/facetsofcomplexity/monday/20200203-C-Peh
 ova.html
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