Wilf-equivalence of patterns 2431 and 3241

Establish that the avoidance counts for the patterns 2431 and 3241 on distinct flattened partitions are equal for every positive integer n, namely, prove that p_n(2431)=p_n(3241) for all n≥1.

Background

The paper classifies the Wilf-equivalence classes for avoidance of single patterns of length four by distinct flattened partitions. Its results determine all equivalence classes of size greater than one except for a possible equivalence between 2431 and 3241. The authors report that the equality of the corresponding avoidance counts has been confirmed numerically through n=14, but leave the general case unresolved. Proving this conjecture would complete the Wilf-classification for length-four patterns in conjunction with the paper’s other results.