A theorem on trees

By A. Cayley. 2009

714 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/1ffbfa8ca6ff57474f808c19f20d1d8fb95941f3

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In Theoretical Computer Science

Citations in the corpus

Spectra of Graphs (2011, background): “The quaternary Hill code ([193]) is a [78, 6, 56] code over F4 with weights 56 and 64.”
DESPOT: Online POMDP Planning with Regularization (2013, background): “One concern, however, is overﬁtting : a policy optimized for ﬁnitely many sampled scenarios may not be optimal in general, as many scenarios are not sampled.”
Spectra of Uniform Hypergraphs (2011, background): “Hence the number of arborescences of Dk is precisely the number of labeled trees on k vertices, which Cayley’s Formula says is kk−2 [8, 25].”
Distribution of shortest path lengths in subcritical Erdős-Rényi networks. (2018, background): “where the binomial coefficient accounts for the number of ways to pick s nodes out of N in order to form a component of size s and the factor of s is the number of distinct tree structures that can be constructed from s distinguishable nodes [64].”
Sequences of regressions and their independences (2011, methodology): “For instance, following the simple enumeration result for labeled trees in d nodes, d, by Karl-Wilhelm Borchardt (1817-1880), it could be shown that these trees are in one-to-one correspondence to distinct strings of size d − 2; see Cayley (1889). Much later, labeled trees were recognized to form th”
Random Complexes and l^2-Betti Numbers (2008, background): “Cayley (1889) evaluated this number in the special case of a complete graph.”
Rational Parking Functions and Catalan Numbers (2014, background): “Two other important objects in combinatorics, trees and parking functions, are counted by the Cayley number (n+ 1)n−1.”
Simplicial matrix-tree theorems (2008, background): “ (2) For 1 ≤i ≤n, let Li be the reduced Laplacian obtained from L by deleting the ith row and ith column. Then τ(G) = detLi. Well-known corollaries of the Matrix-Tree Theorem include Cayley’s formula [9] τ(Kn) = nn−2 (1) where Kn is the complete graph on n vertices, and Fiedler and Sedl´ac¸ek’s form”
Simply generated trees, conditioned Galton–Watson trees, random allocations and condensation (2011, background): “We can often change to an equivalent critical probability weight, but not always.”
About the number of vines and regular vines on n nodes (2010, background): “The first proof about the number of labeled trees on n nodes is due to Cayley in 1889 [12].”