A361014 Triangle read by rows: T(n,k) is the k-th Lie-Betti number of the hypercube graph on 2^(n-1) vertices, n >= 1, k >= 0.

1, 1, 1, 2, 2, 1, 1, 4, 14, 25, 28, 25, 14, 4, 1, 1, 8, 64, 258, 986, 2870, 6134, 11586, 18830, 23832, 25078, 23832, 18830, 11586, 6134, 2870, 986, 258, 64, 8, 1

Offset: 1

Author

Samuel J. Bevins, Feb 28 2023

Keywords

• nonn
• tabf
• more

Examples

			Triangle begins:
   k=0 1  2   3   4    5    6     7     8     9    10    11    12    13   14
n=1: 1 1
n=2: 1 2  2   1
n=3: 1 4 14  25  28   25   14     4     1
n=4: 1 8 64 258 986 2870 6134 11586 18830 23832 25078 23832 18830 11586 6134
...
		

Links

• Marco Aldi and Samuel Bevins, L_oo-algebras and hypergraphs, arXiv:2212.13608 [math.CO], 2022. See page 9.
• Meera Mainkar, Graphs and two step nilpotent Lie algebras, arXiv:1310.3414 [math.DG], 2013. See page 1.
• Eric Weisstein's World of Mathematics, Hypercube Graph.

Crossrefs

Cf. A360571 (path graph), A360572 (cycle graph), A088459 (star graph), A360625 (complete graph), A360936 (ladder graph), A360937 (wheel graph).

Programs

SageMath

# uses[betti_numbers, LieAlgebraFromGraph from A360571]
def A360936_row(n):
    if n == 1: return [1, 1]
    return betti_numbers(LieAlgebraFromGraph(graphs.CubeGraph(n-1)))