3 problems

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Gross–Robbins–Tucker log-concavity conjecture for genus distributions
Let $G$ be a graph, and let $g_k(G)$ denote the number of equivalence classes of 2-cell embeddings of $G$ on the orientable surface of genus $k$ . The sequence…
Conjecturesolvedgenus-distributions graph-embeddings log-concavityarXiv posted 2 days ago
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Log-concavity conjecture for genus distributions of surface-triangulating graphs
Let $G$ be a graph that triangulates some surface, and let its genus distribution be the sequence of numbers of $2$ -cell embeddings of $G$ in orientable surfaces of each genus. Sur…
Conjecturesolvedgenus-distributions graph-embeddings log-concavityarXiv posted 2 days ago
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Liu's unimodality conjecture for genus distributions
Liu's conjecture. The genus distribution of each graph is unimodal.
Conjectureopengenus-distributions graph-theory unimodalityarXiv posted 2 days ago

Gross–Robbins–Tucker log-concavity conjecture for genus distributions