Cyclic-Stack Fibre Candidates

Abstract

The explicit even and odd candidate words are permutations in the target fibre.

The fibre is defined by filtering the complete list of permutations of 1,…,n by equality of the actual stack output to the target. The candidate family is constructed separately. Its words interleave increasing high entries with increasing low entries and leaves one chosen gap empty. Its gap decomposition is literal: the even candidate has no empty gap, while an odd candidate has exactly the selected empty gap.

The target is a permutation of the interval from one through n. Every odd candidate with an admissible omitted gap maps to that target, so all m+1 odd candidates belong to the full fibre. The even candidate does likewise, giving the corresponding lower bound of one.

References

• Dependency: D5/S1/Words/Patterns/CyclicStackPreimagesCore