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Abstract  

We present a new gluing construction for semimodular lattices, related to the Hall-Dilworth construction

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Abstract  

We present an equivalence theorem, which includes all known characterizations of the class B p, i.e., the weight class of Ariño and Muckenhoupt, and also some new equivalent characterizations. We also give equivalent characterizations for the classes B p *, B * and RB p, and prove and apply a “gluing lemma” of independent interest.

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Kinnersley and Langston used a computer search to characterize the class of graphs with path-width at most two. The excluded minor list consists of 110 graphs. This set is fairly large, and the list gives little insight to structural properties of the targeted graph class. We take a different route here. We concentrate on the building blocks of the graphs with path-width at most two and how they are glued together. In this way, we get a short and compact characterization of 2-connected and 2-edge-connected graphs with path-width at most two.

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-1354(98)00463-1 . Beven , K , Freer , J 2001 Equifinality, data assimilation, and uncertainty estimation in mechanistic modelling of complex environmental systems using the GLUE methodology . Journal of Hydrology 249 1–4 11 – 29 10.1016/S0022

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