Some special braids (Q1178081)

The paper deals with the braid semigroup \(S_{n+1}\) given by the presentation \[ \langle \sigma_ 1,\dots,\sigma_ n\mid \sigma_ i \sigma_{i+1} \sigma_ i = \sigma_{i+1} \sigma_ i \sigma_{i+1} (i = 1,\dots,n-1),\;\sigma_ i\sigma_ j = \sigma_ j \sigma_ i\;(i,j = 1,\dots,n,\;| i - j| > 1)\rangle \] analogous to that of Artin's \(n\)-generated braid group. The author establishes certain connections between some elements of \(S_{n+1}\) widely used by researchers such as segments, fundamental braids, crosses and so on. These connections may be useful in investigations of transformations of words in a braid group.