A bracelet is the lexicographically smallest element in an equivalence class of strings under string rotation and reversal. We present a fast, simple, recursive algorithm for generating (i.e., listing) k-ary bracelets. Using simple bounding techniques, we prove that the algorithm is optimal in the sense that the running time is proportional to the number of bracelets produced. This is an improv...

The Lucas numbers, 2, 1, 3, 4, 7, 11, 18, 29, 47, . . . , named in honor of Edouard Lucas (1842-1891), are defined by L0 = 2, L1 = 1, and Ln = Ln−1 + Ln−2 for n ≥ 2. It is easy to show that, for n ≥ 1, Ln counts the ways to create a bracelet of length n using beads of length one or two, where bracelets that differ by a rotation or a reflection are still considered distinct. For example, there a...

The identity linking the Tutte polynomial with the Potts model on a graph implies the existence of a decomposition resembling that previously obtained for the chromatic polynomial. Specifically, let {Gn} be a family of bracelets in which the base graph has b vertices. Then the Tutte polynomial of Gn can be written as a sum of terms, one for each partition π of a non-negative integer ` ≤ b: (x− ...

Harlow T, Greaves C, White A, et al. Randomised controlled trial of magnetic bracelets for relieving pain in osteoarthritis of the hip and knee. BMJ 2004;329:1450–4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....

OBJECTIVE To evaluate whether hospitalised patients would agree to wear an identification bracelet and whether patient acceptability is improved by more detailed explanations or by using a code instead of a name on the bracelet. DESIGN Patient survey that tested two variables in a randomised factorial design. Explanations about identification bracelets were given (a) with or without examples ...

We show that the twisted SL2 skein algebra of a surface has a natural basis (the bracelets basis) that is positive, in the sense that the structure constants for multiplication are positive integers.