On the Four Parameters of L-shape Tile Determined by a Directed Double Loop Network G(n;s_1,s_2)
Baoxing Chen · 2006
Given a directed double loop network G(n;s1,s2),four parameters k1,k2,j1,j2 are defined are follows:(1)k1=min{k | ks2≡js1(mod n) and k ≥ j ≥ 0,k=1,2,…,n-1};(2)j1=min{j | k1s2≡js1(mod n),j ≥ 0};(3)j2=min{j | ks2≡js1(mod n) and jk ≥ 0,j=1,2,…,n-1};(4)k2=min{k | ks2≡j2s1(mod n),k ≥ 0}.We prove that k1,k2,j1,j2 are four parameters of the L-shape tile determined by the network G(n;s1,s2) and(j2-j1,k1-k2) is the least positive solution of xs1+ys2 ≡0(mod n).