For , we have where is the set of -matrices, is the number of ‘s in , and is the matrix formed by deleting the -th column of .

For , we have where is the set of -matrices, is the number of ‘s in , and is the matrix of minors satisfying for all .

Since the proofs are cumbersome and my WordPress LaTeX skills are not great, I wrote up what I’ve done at Overleaf: https://www.overleaf.com/8425738kswcbnfsfzqw

]]>I just stumbled upon the surprising property: for , this sequence has the property that What’s up with that?! I find it hard to believe this is just a small-case numerical coincidence, since when we have which are some big numbers.

In Stones and Wanless (2012), we conjectured for all n. If the above observation is true for all even n, then the Alon-Tarsi Conjecture also implies our conjecture. I.e., the two conjectures are equivalent.

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