In earlier work it was shown that each nonabelian finite simple group G has a conjugacy class C such that, whenever 1 = x ∈G, the probability is greater than 1/10 that G= 〈x, y〉 for a random y ∈ C. Much stronger asymptotic results were also proved. Here we show that, allowing equality, the bound 1/10 can be replaced by 13/42; and, excluding an explicitly listed set of simple groups, the bound 2...

This paper arose out of an attempt to generalize the ’q; q−1“-basis for the centre of an Iwahori–Hecke algebra Hq found by Jones to ’q; q−1“ and to other types. Considering the Iwahori–Hecke algebra H over a subring ’ξ“ of ’q1/2; q−1/2“, where ξ = q1/2 − q−1/2, we use a new and natural definition of positivity on H to describe the “minimal” ’ξ“-basis for ZH‘ in terms of a partial order on the ...

A one-sided (resp. two-sided) shift of finite type of dimension one can be described as the set of infinite (resp. bi-infinite) sequences of consecutive edges in a finite-state automaton. While the conjugacy of shifts of finite type is decidable for one-sided shifts of finite type of dimension one, the result is unknown in the two-sided case. In this paper, we study the shifts of finite type de...