Strong log-convexity of genus sequences

Mohar, Bojan (avtor)

For 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.

• Jezik: Angleški jezik
• Ključne besede: graphs on surfaces, 2-cell embedding, genus distribution, log-concavity, Log Concavity Conjecture
• Vrsta gradiva: Članek v reviji
• Tipologija: 1.01 - Izvirni znanstveni članek
• Organizacija: FMF - Fakulteta za matematiko in fiziko
• Status publikacije: Objavljeno
• Različica publikacije: Objavljena publikacija
• Datum objave: 01.05.2026
• Leto izida: 2026
• Št. strani: Str. 164-179
• Številčenje: Vol. 178
• PID: 20.500.12556/RUL-177835
• UDK: 519.17
• ISSN pri članku: 0095-8956
• DOI: 10.1016/j.jctb.2025.12.005
• COBISS.SI-ID: 264051715
• Datum objave v RUL: 09.01.2026

Gradivo je del revije

• Naslov: Journal of combinatorial theory. Series B
• Skrajšan naslov: J. comb. theory, Ser. B
• Založnik: Elsevier
• ISSN: 0095-8956
• COBISS.SI-ID: 25721600

Licence

• Licenca: CC BY 4.0, Creative Commons Priznanje avtorstva 4.0 Mednarodna
• Povezava: http://creativecommons.org/licenses/by/4.0/deed.sl
• Opis: To je standardna licenca Creative Commons, ki daje uporabnikom največ možnosti za nadaljnjo uporabo dela, pri čemer morajo navesti avtorja.

Projekti

• Financer: NSERC - Natural Sciences and Engineering Research Council of Canada
• Program financ.: Discovery Grant
• Številka projekta: R832714

• Financer: EC - European Commission
• Številka projekta: 101071836
• Naslov: KARST: Predicting flow and transport in complex Karst systems
• Akronim: KARST