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Recall that the nilCoxeter algebra $\mathcal{N}_W$ for a Coxeter group $W$ is given by the $\mathbf{k}$-basis $x_w$ for each $w\in W$ and multiplication $x_ux_v=x_{uv}$ if $\ell(uv)=\ell(u)+\ell(v)$ ...

How can k permutations on n-set be arranged to maximize minimal pairwise Kendall tau distance (i.e. number of discordant pairs) between them? For two permutations this is obviously when the second ...