20 Apr
2018
20 Apr
'18
1:21 p.m.
similar but with a twist: say I generated the set of bracelets (necklaces with reversal) of 0 or 1 with n beads, with no more than floor(n/2) beads equal to 1. Define the polynomial 'p' of the bracelet as Sum(k=index of 1 in the bracelet position; z^k). Then, can I define a 'leader' bracelet such that appending any number m of extra 0-beads to it (resulting in a bracelet with n+m beads) has the same 'leader bracelet' polynomial p? In other words, can there exist an ordering of such (0-1) strings where the least element is is unchanged by appending zero's?