Weighted lattice paths
نویسندگان
چکیده
منابع مشابه
Asymmetric Exclusion Model and Weighted Lattice Paths
We show that the known matrix representations of the stationary state algebra of the Asymmetric Simple Exclusion Process (ASEP) can be interpreted combinatorially as various weighted lattice paths. This interpretation enables us to use the constant term method (CTM) and bijective combinatorial methods to express many forms of the ASEP normalisation factor in terms of Ballot numbers. One particu...
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Lemma 1.1. Consider a (directed) weighted graph G = (V, E), w : E → R+ ∪ {0} with no negative edge weights, a source vertex s and an arbitrary distance value d ∈ R+ ∪ {0}. Let X = X ′ ∪ X ′′ , where X ′ = {v ∈ V : δ(s, v)< d} be the set of vertices that are less than d from s, X ′′ ⊆ {v ∈ V : δ(s, v) = d} be the set of vertices that are exactly d from s. Also, let d ′ = min{δ(s, u) : u ∈ V \ X ...
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Developing from a concern in bioinformatics, this paper analyses alternative metrics between partitions. From both theoretical and applicative perspectives, a seemingly most appropriate distance between any two partitions is HD, which counts the number of atoms finer than either one but not both. While faithfully reproducing the traditional Hamming distance between subsets, HD is very sensible ...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1971
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1971.37.85