ar X iv : 0 71 1 . 16 95 v 1 [ m at h . C O ] 1 2 N ov 2 00 7 Minimum de Bruijn Sequence in a Language with Forbidden Substrings

ar X iv : 0 71 1 . 26 95 v 1 [ m at h . SP ] 1 6 N ov 2 00 7 REGULARITY AND THE CESÀRO – NEVAI CLASS

We consider OPRL and OPUC with measures regular in the sense of Ullman–Stahl–Totik and prove consequences on the Jacobi parameters or Verblunsky coefficients. For example, regularity on [−2, 2] implies lim N →∞ N −1 [ N n=1 (a n −1) 2 +b 2 n ] = 0.

ar X iv : 0 71 1 . 23 72 v 1 [ m at h . G R ] 1 5 N ov 2 00 7 Braid groups and Artin groups

ar X iv : m at h . C O / 0 41 16 10 v 1 2 7 N ov 2 00 4 CHAIN POLYNOMIALS OF DISTRIBUTIVE LATTICES ARE 75 %

It is shown that the numbers ci of chains of length i in the proper part L \ {0, 1} of a distributive lattice L of length l + 2 satisfy the inequalities c0 < . . . < c⌊l/2⌋ and c⌊3l/4⌋ > . . . > cl. This proves 75 % of the inequalities implied by the Neggers unimodality conjecture.

ar X iv : 0 71 1 . 32 82 v 1 [ he p - ph ] 2 1 N ov 2 00 7 Study of Pure Annihilation Decays B d , s → D 0 D 0

With heavy quark limit and hierarchy approximation λ QCD ≪ m D ≪ m B , we analyze the

ar X iv : 0 71 1 . 14 20 v 1 [ m at h . O A ] 9 N ov 2 00 7 Finite - dimensional Hopf C - bimodules and C - pseudo - multiplicative unitaries

Finite quantum groupoids can be described in many equivalent ways [8, 11, 16]: In terms of the weak Hopf C -algebras of Böhm, Nill, and Szlachányi [2] or the finite-dimensional Hopf-von Neumann bimodules of Vallin [14], and in terms of finite-dimensional multiplicative partial isometries [4] or the finite-dimensional pseudo-multiplicative unitaries of Vallin [15]. In this note, we show that in ...