The monodromy pairing and discrete logarithm on the Jacobian of finite graphs

DOI10.1515/JMC.2010.002zbMath1231.05173arXiv0907.4764OpenAlexW3099502112MaRDI QIDQ3580731

Farbod Shokrieh

Publication date: 13 August 2010

Published in: Journal of Mathematical Cryptology (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0907.4764

zbMATH Keywords

Jacobiangraphscritical groupgeneralized inversesdiscrete logarithmsandpilesmonodromy pairing

Mathematics Subject Classification ID

Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Jacobians, Prym varieties (14H40) Computational number theory (11Y99)

Related Items (14)

The distribution of sandpile groups of random graphs ⋮ Divisors on graphs, binomial and monomial ideals, and cellular resolutions ⋮ The sandpile group of a thick cycle graph ⋮ Geometric bijections for regular matroids, zonotopes, and Ehrhart theory ⋮ On a Cohen-Lenstra heuristic for Jacobians of random graphs ⋮ The critical groups of Adinkras up to 2-rank of Cayley graphs ⋮ Two-vertex generators of Jacobians of graphs ⋮ Chip-Firing Games and Critical Groups ⋮ Critical groups of simplicial complexes ⋮ Realization of groups with pairing as Jacobians of finite graphs ⋮ Canonical measures on metric graphs and a Kazhdan's theorem ⋮ A note on Brill-Noether existence for graphs of low genus ⋮ GEOMETRIC BIJECTIONS FOR REGULAR MATROIDS, ZONOTOPES, AND EHRHART THEORY ⋮ A Note on Jacobians, Tutte Polynomials, and Two-Variable Zeta Functions of Graphs

Cites Work

• Critical groups for homeomorphism classes of graphs
• Self-organized criticality
• The lattice of integral flows and the lattice of integral cuts on a finite graph
• Self-organized critical state of sandpile automaton models

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