Figure 2
Diagram representation and irreducibility. A diagram over {1,…,55}. The arcs (1,21) and (11,33) are crossing and the dashed arc (9,10) is a 1-arc which is not allowed. This structure contains 4 stacks with length 7, 4, 6 and 4, from left to right respectively. Irreducibility relative also to a decomposition rule. The rule Λ∗ splitting Si,j to Si,k and Sk + 1,j, S1,55 is not Λ∗-irreducible, while S2,40 and S43,55 are. However, for a specific decomposition rule Λ, which removes the outmost arc, S43,55 is not Λ-irreducible while S2,40 is.