I'm currently working on what I hope will be part the work for my dissertation defense for my Mathematics Ph.D. The work eventually had permutations pop up, but the process I am applying to the permutations is coming up with a statistic that I couldn't find a pattern in. I decided to use FindStat, and it told me that my numbers were consistent with "the dissociation number of the complement graph of the de-duplicated graph of the inversion graph given by the permutation."

The numbers are correct up to at least permutations of length 5, and at least some of the permutations of length 6. At this point, I have stopped checking individual numbers to see if they are correct.

The question resolves "YES" if I am able to prove that my permutation statistic is indeed equal to "the dissociation number of the complement graph of the de-duplicated graph of the inversion graph given by the permutation." This question will resolve "NO" if I find a counterexample, I hit the close date for the question and I have moved on from the conjecture with no plans to return to it in the near future, or if I someone else proves the conjecture and I am not actively involved in generating the proof.

If I hit the close date and I am still working on the problem or believe I will return to it soon, I will extend the date.

I will not bet on this market.