isCartwrightSturmfels -- whether a permutation is Cartwright-Sturmfels

Given a permutation in 1-line notation, checks if the permutation is Cartwright-Sturmfels. By [CDG22], the matrix Schubert variety $X_w$ is Cartwright-Sturmfels if and only if $w$ avoids all of the patterns $\{12543, 13254, 13524, 13542, 21543, 125364, 125634, 215364, 215634, 315264, 315624, 315642\}$.

• [CDG22] A. Conca, E. De Negri, and E. Gorla, Radical generic initial ideals, Vietnam J. Math. 50 (2022), no. 3, 807-827.

i1 : w = {7,2,5,8,1,3,6,4}

o1 = {7, 2, 5, 8, 1, 3, 6, 4}

o1 : List

i2 : isCartwrightSturmfels w

o2 = false

i3 : v = {1,6,9,2,4,7,3,5,8}

o3 = {1, 6, 9, 2, 4, 7, 3, 5, 8}

o3 : List

i4 : isCartwrightSturmfels v

o4 = false