Convolution Preserves Partial Synchronicity of Log-concave Sequences

H. Hu; David G. L. Wang; F. Zhao; T. Y. Zhao

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arXiv · 1507.08430

Convolution Preserves Partial Synchronicity of Log-concave Sequences

H. Hu·David G. L. Wang·F. Zhao·T. Y. Zhao

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Abstract

In a recent proof of the log-concavity of genus polynomials of some families of graphs, Gross et al. defined the weakly synchronicity relation between log-concave sequences, and conjectured that the convolution operation by any log-concave sequence preserves weakly synchronicity. We disprove it by providing a counterexample. Furthermore, we find the so-called partial synchronicity relation between log-concave sequences, which is (i) weaker than the synchronicity, (ii) stronger than the weakly synchronicity, and (iii) preserved by the convolution operation.

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BibTeX RIS

H. Hu, David G. L. Wang, F. Zhao, T. Y. Zhao. 2015-07-31. Convolution Preserves Partial Synchronicity of Log-concave Sequences. https://arxiv.org/abs/1507.08430

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