On standard locally catenative L schemes (Q807025)

Let \(<\Sigma,h,w>\) be a DOL system and \(w_ 0,w_ 1,...,w_ n,.\). its generating sequence. A DOL system \(G=<\Sigma,h,w>\) is said to be \(<i_ 1,i_ 2,...i_ k>\)-locally catenative (l-c) with cut p if \(w_ q=w_{q-i_ 1}w_{qi_ 2}...w_{qi_ k}\) for any \(q\geq p\) \((k\geq 2,p,i_ 1,...,i_ k\geq 1)\). The standard \(<i_ 1,i_ 2,...,i_ k>\) locally catenative L scheme is a DOL scheme \(S=(\Sigma_ n,h)\) where \(n=\max \{i_ 1,i_ 2,...,i_ k\}\), \(\Sigma_ n=\{0,1,2,...,n-1\}\), \(h(i)=i+1\) \(0\leq i\leq n-2\) and \(h(n-1)=(n-i_ 1)(n-i_ 2)...(n-i_ k)\). The L system \(G=<\Sigma_ n,h,0>\) is called the primary L system of S. In this paper three sufficient conditions for standard l-c L-scheme having multiple l-c L-systems, are presented. These schemes are defined as parallel decomposable L-schemes, cyclic L-schemes and semicyclic L- schemes respectively.