Fig 6 - uploaded by Walter Whiteley
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![A minimal 1-cycle in R 3 (n) and K 1 2 (n), with β 1 = 0 (A), formed by a 'circuit exchange' on two smaller 1-cycles with opposite coefficients on a shared edge [a, b] (B).](profile/Walter-Whiteley/publication/342870668/figure/fig4/AS:912149459243008@1594484786088/A-minimal-1-cycle-in-R-3-n-and-K-1-2-n-with-b-1-0-A-formed-by-a-circuit.png)
A minimal 1-cycle in R 3 (n) and K 1 2 (n), with β 1 = 0 (A), formed by a 'circuit exchange' on two smaller 1-cycles with opposite coefficients on a shared edge [a, b] (B).
Source publication
From recent work in two areas of discrete applied geometry, we abstract a common pattern of families of geometric homologies for graphs realized in projective d-space (for static rigidity) or in the projective plane (for bivari-ate splines). Using distinct algebraic constructions for the local coefficients of the chain complexes (exterior algebra f...
Context in source publication
Context 1
... absence of a combinatorial characterization (and corresponding polynomial-time algorithms for acyclic sets) reflects a number of differences between these chain complexes and R 2 (G) ≡ K 0 1 (G). Figure 6A shows a nonrigid minimal 1-cycle. Alternately, the submodular function f (E) = 3|V | − 6 is 0 on single edges and does not define a useful matroid on the edges [24]. ...
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