A combinatorial approach for the state complexity of the Shuffle product

We investigate the state complexity of the shuffle operation on regular languages initiated by Campeanu et al. and studied subsequently by Brzozowski et al. We shift the problem into the combinatorics domain by turning the problem of state accessibility into a problem of intersection of partitions. This allows us to develop new tools and to reformulate the conjecture of Brzozowski et al. about the above-mentionned state complexity.