Strong log-convexity of genus sequencesMohar, Bojan (Avtor) graphs on surfaces2-cell embeddinggenus distributionlog-concavityLog Concavity ConjectureFor a graph $G$, and a nonnegative integer $g$, let $a_g(G)$ be the number of $2$-cell embeddings of ▫$G$▫ in an orientable surface of genus $g$ (counted up to the combinatorial homeomorphism equivalence). In 1989, Gross, Robbins, and Tucker [Genus distributions for bouquets of circles, J. Combin. Theory Ser. B 47 (1989), 292-306] proposed a conjecture that the sequence $a_0(G), a_1(G), a_2(G), \dots$ is log-concave for every graph $G$. This conjecture is reminiscent to the Heron-Rota-Welsh Log Concavity Conjecture that was recently resolved in the affirmative by June Huh et al., except that it is closer to the notion of $\Delta$-matroids than to the usual matroids. In this short paper, we disprove the Log Concavity Conjecture of Gross, Robbins, and Tucker by providing examples that show strong deviation from log-concavity at multiple terms of their genus sequences.20262026-01-09 09:16:53Članek v reviji177835UDK: 519.17ISSN pri članku: 0095-8956DOI: 10.1016/j.jctb.2025.12.005COBISS_ID: 264051715sl