2017/12/11 by Guantao Chen, Chen, Guantao, Serguei Norine +5
Computer Science · Engineering · Mathematics · #Advanced Differential Equations and Dynamical Systems #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.1712.03869
openalex publication_date 2017/12/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let G=(V,E) be a finite undirected graph. If P is an oriented path from r1∈ V to r2∈ V, we define ∂(P) = r2-r1. If R, S⊆ V, we denote by P(G; R, S) the span of the set of all ∂ P⊗ ∂ Q with P and Q disjoint oriented paths of G connecting vertices in R and S, respectively. By L(R, S), we denote the submodule of ℤ⟨ R⟩⊗ℤ⟨ S⟩ consisting all ∑r∈ R, s∈ S c(r,s)r⊗ s such that c(r,r) = 0 for all r∈ R∩ S, ∑r∈ R c(r, s) = 0 for all s∈ S, and ∑s∈ S c(r, s) = 0 for all r∈ R. In this paper, we provide, when G is sufficiently connected, characterizations when P(G; R, S) is a proper subset of L(R, S).