A347976 Triangle T(n,k) read by rows: the rows list volumes of rank 2 Schubert matroid polytopes.
1, 2, 4, 3, 8, 11, 4, 13, 22, 26, 5, 19, 38, 52, 57, 6, 26, 60, 94, 114, 120, 7, 34, 89, 158, 213, 240, 247, 8, 43, 126, 251, 376, 459, 494, 502, 9, 53, 172, 381, 632, 841, 960, 1004, 1013, 10, 64, 228, 557, 1018, 1479, 1808, 1972, 2026, 2036, 11, 76, 295, 789, 1580, 2503, 3294, 3788, 4007, 4072, 4083
Offset: 3
Examples
The triangle T(n,k) starts as follows: [n\k] [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [3] 1; [4] 2, 4; [5] 3, 8, 11; [6] 4, 13, 22, 26; [7] 5, 19, 38, 52, 57; [8] 6, 26, 60, 94, 114, 120; [9] 7, 34, 89, 158, 213, 240, 247; [10] 8, 43, 126, 251, 376, 459, 494, 502; [11] 9, 53, 172, 381, 632, 841, 960, 1004, 1013; [12] 10, 64, 228, 557, 1018, 1479, 1808, 1972, 2026, 2036; [13] 11, 76, 295, 789, 1580, 2503, 3294, 3788, 4007, 4072, 4083; [14] 12, 89, 374, 1088, 2374, 4089, 5804, 7090, 7804, 8089, 8166, 8178; ...
Links
- Carolina Benedetti, Kolja Knauer, and Jerónimo Valencia-Porras, On lattice path matroid polytopes: alcoved triangulations and snake decompositions, arXiv:2303.10458 [math.CO], 2023.
Crossrefs
Formula
T(n,k-1) + T(n,k) + k = T(n+1,k).
For a fixed k, the column T(n,k) is given by a polynomial in n.
For any 1 <= k <= n-3, T(n,k) + T(n,n-k-2) = T(n,n-2).
Comments