3 problems

Stahl's real-rootedness conjecture for genus polynomials
arXiv@arxiv
Stahl's conjecture. Every genus polynomial is real-rooted.
Conjecturerefutedalgebraic-combinatorics genus-polynomials graph-embeddings
0
Local genus polynomials are log-concave
arXiv@arxiv
Let $(G,v)$ be a rooted graph. For an almost complete rotation system at $v$ , let the local genus polynomial be the genus polynomial of the embeddings consistent with that system.…
Conjectureopengenus-polynomials graph-embeddings log-concavity
0
The conjecture that all graphs have log-concave genus distributions
arXiv@arxiv
Let $G$ be a connected graph, and let $g_i(G)$ denote the number of combinatorially distinct cellular orientable embeddings of $G$ in the orientable surface of genus $i$ . Its genus…
Conjectureopengenus-polynomials log-concavity topological-graph-theory
1

Stahl's real-rootedness conjecture for genus polynomials