Philosophy@Work

“We deal with atoms and bonds: a bond is a (perhaps directed) path between two atoms. An n-stepped walk is an ordered connected path along n consecutive bonds, each step being in the permitted direction of a bond (if the bond in question is directed) and starting from the atom reached by the previous step (if any). W_n(A) denotes a typical n-stepped walk starting from an atom A. A walk is self-avoiding if it visits no atom more than once. S_n(A) denotes a self-avoiding W_n(A). Two walks are distinct if they do not utilize the same set of bonds, with due regard to order. f_A(n, r) denotes the number of distinct W_n(A), each of which can be broken into r or fewer self-avoiding subwalks. In particular we write f_A(n) =f_A(n, 1) for the number of distinct S_n(A). Two atoms A and B are outlike if f_A(n) = f_B{n) for all n. An outlike class is a class of pairwise outlike atoms. A crystal is an infinite set of atoms and bonds satisfying the three postulates” (p. 642) #Hammersley #atom #bond #walk #crystal