OFFSET
1,4
COMMENTS
a(n) is also the number of non-isomorphic MAT-labelings of complete graph K_n. (Tran, Tran, Tsujie, 2024, Theorem 3.1).
From Shuhei Tsujie, May 22 2026: (Start)
a(n) is also the number of non-isomorphic maximal Arrow's single-peaked domains.
a(n) is also the number of non-isomorphic (n,3)-extremal lattices. (End)
REFERENCES
H. Joe, R. M. Cooke, and D. Kurowicka, Regular Vines: Generation Algorithm and Number of Equivalence Classes, in D. Kurowicka and H. Joe, eds., Dependence Modeling, World Scientific, 2010, pp. 219-231 (§10.3).
H. M. Tran, T. N. Tran, and S. Tsujie, Vines and MAT-labeled graphs, Forum of Mathematics, Sigma, Vol. 12 (2024), Art. e128.
LINKS
Shuhei Tsujie, Table of n, a(n) for n = 1..83
Bogdan Chornomaz, Counting extremal lattices, HAL Preprint hal-01175633, 2015.
Klas Markström, Søren Riis, and Bei Zhou, Arrow's single peaked domains, richness, and domains for plurality and the Borda count, arXiv:2401.12547 [econ.TH], 2024.
Hung Manh Tran, Tan Nhat Tran, and Shuhei Tsujie, Vines and MAT-labeled graphs, Séminaire Lotharingien de Combinatoire 91B (2024) Article #12, 12 pp.
Hung Manh Tran, Tan Nhat Tran, and Shuhei Tsujie, An axiomatic framework from splitting and merging in MAT-labeled graphs, vines, and single-peaked domains, arXiv:2605.20629 [math.CO], 2026.
FORMULA
a(1) = a(2) = a(3) = 1; for n >= 4, a(n) = 2^((n-2)*(n-3)/2 - 1) * Sum_{k=0..m} c(k) * 2^(-k*(n-k-2)), where m = floor(n/2) - 1, and c(k) = 2 if k = m else 1. - Shuhei Tsujie, May 22 2026
CROSSREFS
KEYWORD
nonn
AUTHOR
Thomas Zaslavsky, Jan 03 2025
EXTENSIONS
More terms from Shuhei Tsujie, May 22 2026
STATUS
approved