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{} = Brackets used in Arrays

a = First entry in Array

b = Second entry in Array

c = Last entry in Array

X = An Array

X' = An Array

X" = An Array

a(b) = a inside a b-gon (Steinhaus-Moser Notation)


  • {a} = a
  • {X,1,X'} = {X}
  • {X,1,X',1,X"} = {X}
  • {X,1} = {X}
  • {X,0,X'} = {X,X'}
  • {a,b} = a(b)
  • {a,b,c} = {a+1,{a,b-1,c},c-1}
  • {a,b,X,c} = {a+1,{a,b-1,X,c},X,c-1}

In words


  • If a is the only entry, then the array equals a
  • Any single 1's are cropped off with anything behind it.
  • If there are multiple single 1's, the most leftward single 1 and anything behind it are cropped off.
  • If the last entry is 1, the 1 is cropped off.
  • Any 0's are cropped off.
  • {a,b} equals a inside a b-gon in teh Steinhaus-Moser Notation.
  • If there are three or more entires, degenerate by adding 1 to the a, replacing b with the copy of the original array except b-1, and decrease c by 1.

Also any 1's that are not single like {5,1,1,4,1,1,1,3} are converted into a.

e.g. {5,1,1,1,1,4} = {5,5,5,5,5,4}

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