A259116 Number of unrooted binary unordered tanglegrams of size n.

1, 1, 1, 2, 4, 22, 145, 1875, 31929, 698183, 18056523, 538340256, 18141423039, 681939320185

Offset: 1

Author

Frederick A. Matsen IV, Jun 18 2015

Keywords

• nonn
• more

Comments

Binary tanglegrams are pairs of bifurcating (degree 3 internal node) trees with a bijection between the leaves of the trees. Two tanglegrams are isomorphic if there is an isomorphism between the trees that preserves the bijection. Unrooted means that the tanglegram is composed of unrooted trees, and unordered means that two tanglegrams that differ by exchanging the trees and inverting the bijection are considered identical.

Links

• S. C. Billey, M. Konvalinka, and F. A. Matsen IV, On the enumeration of tanglegrams and tangled chains, arXiv:1507.04976 [math.CO], 2015.
• Ira M. Gessel, Counting tanglegrams with species, arXiv:1509.03867 [math.CO], (13-September-2015)
• F. A. Matsen IV, S. C. Billey, D. A. Kas, and M. Konvalinka, Tanglegrams: a reduction tool for mathematical phylogenetics, arXiv:1507.04784 [q-bio.PE], 2015.
• Frederick A. Matsen, Sage/GAP4 Code for generating tanglegrams

Crossrefs

Cf. A258620 (tanglegrams), A259114, A259115, A258486 (tangled chains), A258487, A258488, A258489.

Extensions

More terms from Ira M. Gessel, Jul 19 2015