▁hypothesis . ▁ ▁Rank ▁of ▁a ▁partition ▁ ▁In ▁number ▁theory ▁and ▁combin ator ics ▁rank ▁of ▁a ▁partition ▁of ▁a ▁positive ▁integer ▁is ▁a ▁certain ▁integer ▁associated ▁with ▁the ▁partition . ▁D ys on ▁introduced ▁the ▁concept ▁in ▁a ▁paper ▁published ▁in ▁the ▁journal ▁E ure ka . ▁It ▁was ▁presented ▁in ▁the ▁context ▁of ▁a ▁study ▁of ▁certain ▁con gru ence ▁properties ▁of ▁the ▁partition ▁function ▁discovered ▁by ▁the ▁math ematic ian ▁S rin iv asa ▁Ram an uj an . ▁ ▁C rank ▁of ▁a ▁partition ▁ ▁In ▁number ▁theory , ▁the ▁c rank ▁of ▁a ▁partition ▁is ▁a ▁certain ▁integer ▁associated ▁with ▁the ▁partition ▁in ▁number ▁theory . ▁D ys on ▁first ▁introduced ▁the ▁term ▁without ▁a ▁definition ▁in ▁a ▁ 1 9 4 4 ▁paper ▁in ▁a ▁journal ▁published ▁by ▁the ▁Mathemat ics ▁Society ▁of ▁Cambridge ▁University . ▁He ▁then ▁gave ▁a ▁list ▁of ▁properties ▁this ▁yet - to - be - defined ▁quantity ▁should ▁have . ▁In ▁ 1 9 8 8 , ▁George ▁E . ▁Andrew s ▁and ▁Frank ▁Gar van ▁discovered ▁a ▁definition ▁for ▁the ▁c rank ▁satisfying ▁the ▁properties ▁D ys on ▁had ▁hypoth es ized . ▁ ▁Ast ro ch icken ▁ ▁Ast ro ch icken ▁is ▁the ▁name ▁given ▁to ▁a ▁thought ▁experiment ▁D ys on ▁exp ounded ▁in ▁his ▁book ▁Dist urb ing ▁the ▁Un iverse ▁( 1 9 7 9 ). ▁He ▁cont empl ated ▁how ▁human ity ▁could ▁build ▁a ▁small , ▁self - rep lic ating ▁automat on