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Sperner's Theorem Theorem(Sperner 1928) F C 2 is an antichain. (2) Emanuel Sperner (1905-1980)        '$ #   $  " $   "$ ($ ' ' ($  2   $  $#$'#   ( $*   0 ) $"" #"$ #$ * # 2   '  $  .% .$0  " #$  1 ''$ "    '$' $$ $ ' - $ $ "* #' ($$#  0 (  '+  ' (  $$#' + ( $' " $   $    $#  0 3/4 ,'$ #  $! $$"   ##"  2 -  " $     0 $##$$'#  (  $      $$   $'# 0 )$   $#$ $$7 # $#+ $'# $## - $*   $$  "  ! " 0!$ '$&'' ('$# * 6 $ 34 8" # $   $$$  ! ! " "  ! " 0  5  '"$ $  $ #$  0         ! ! " " !   '$  ##" + $  ( ##+  ($ (#  $' # $0  ( $$ ($$$0  " $ "  ≤ ! ! " " 0 !  $"      (  ∅ ⊂ ⊂ ⊂ ⊂ +"    0"'$$$   7 # $#+"  ($ $$ ($ (  # '  +  $ $'$ $$  $ '$ +$' # 0 &+$  ∈ " $!"'$  $$ 0$ $0  ' ∅  " $ $ # '   ( +$  $ '  " $ $  '$ # ' 0 $ # ' +  ( $##  $$#!   "  $  $   #  −  $0  $$$ $"    $  + $$$0 ' #   +#  # (  ' (  -  0   0 ##"'$ ' ( $ $' ' ' (   $   −  $ &  $ &  ' (    $0  |F| ￾ ￾ n ⇤n/2⌅ ⇥ . Theorem (Sperner 1928) |F| ￾ ￾ n ⇤n/2⌅ ⇥ . Theorem (Sperner 1928) F ￾ 2[n] is an antichain. Sperner’s Theorem Emanuel Sperner (1905 - 1980)
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