isCDG -- whether a permutation is CDG

Given a permutation in 1-line notation, checks if the permutation is CDG. We say that a permutation $w$ is CDG if a certain modification (see [Kle23] for precise description) of the Fulton generators of the Schubert determinantal ideal $I_w$ form a diagonal Gröbner basis. By [Kle23], $w$ is CDG if and only if $w$ avoid all of the patterns $\{13254, 21543, 214635, 215364, 215634, 241635, 315264, 4261735\}$.

• [Kle23] P. Klein, Diagonal degenerations of matrix Schubert varieties, Algebr. Comb. 6 (2023), no. 4, 1073-1094.

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

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

o1 : List

i2 : isCDG w

o2 = true

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

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

o3 : List

i4 : isCDG v

o4 = true