On ordered $k$-paths and rims for certain families of Kazhdan-Lusztig cells of $S_n$

T. P. McDonough, C. A. Pallikaros

For a composition $\lambda$ of $n$ we consider the Kazhdan-Lusztig cell in the symmetric group $S_n$ containing the longest element of the standard parabolic subgroup of $S_n$ associated…