2013/05/22 by Natalie Aisbett, Aisbett, Natalie
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #math.CO
paper · pdf · doi:10.48550/arxiv.1305.5128
arxiv created 2014/01/08 · arxiv updated 2014/01/09
Rudolph conjectures that for permutations p and q of the same length, An(p) ≤ An(q) for all n if and only if the spine structure of T(p) is less than or equal to the spine structure of T(q) in refinement order. We prove one direction of this conjecture, by showing that if the spine structure of T(p) is less than or equal to the spine structure of T(q), then An(p) ≤ An(q) for all n. We disprove the opposite direction by giving a counterexample, and hence disprove the conjecture.