A proof of a conjecture of Buck, Chan, and Robbins on the expected value of the minimum assignment

By Johan Wästlund. 2005

118 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/a734568626895c40bd7f09bf9740be2225617850

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In Computational Theory and Mathematics

In Discrete Mathematics and Combinatorics

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Citations in the corpus

Limit laws for functions of fringe trees for binary search trees and random recursive trees (2015, methodology): “Theorem 8.6 includes several earlier results, proved by several different methods: (8.10) was shown by Mahmoud and Ward [35] for ` = 2 and by Bóna [6] and Devroye and Janson [12] in general; [35] also shows (8.11)–(8.12) for ` = 2; (8.13) was shown by Mahmoud and Ward [36] for ` = 2 and by Devroye ”
Regularity Lemma for k‐uniform hypergraphs (2004, background): “On the other hand, in the k-uniform hypergraph case, this is a very technical statement which has been proved for k = 3 in [9] and for k = 4 in [ 12 , 13].”
Random Graphs and Complex Networks (2016, unknown): “15 (Degree sequence uniform recursive tree [145]).”
Functional limit theorems for multitype branching processes and generalized Pólya urns (2004, unknown): “The process UI is real, while the processes Uλ,k and variables Wλ are real for real λ but complex otherwise, with Uλ̄,k = Uλ,k and Wλ̄ = Wλ.”
Plane recursive trees, Stirling permutations and an urn model (2008, background): “(In fact, they proved joint asymptotic normality of Nnd (d ≤ 2), which was extended in [10] to all d, see also [9, Example 7.”
Fringe trees, Crump-Mode-Jagers branching processes and $m$-ary search trees (2016, background): “Since the Laplace transform transforms convolutions to multiplications, and ∫∞ 0 f(t)e −t dt = E e−Sm−1 = 1/m by (7.9), we have by (10.8) also the alternative formula (that might be better for numerical calculations) Pk = 2 m ∫ ∞ 0 e−t ( (hk−1(t) + e −t)m − e−mt ) dt. (10.12) In the binary case m = ”
An inverse theorem for the Gowers U^3 norm (2005, methodology): “ntially closer in spirit to Roth’s original argument than the other proofs. Even more recently there have been a number of other proofs of this theorem by other methods, such as hypergraph regularity [27, 45, 46, 50, 51, 52] or “discrete ergodic theory” [59]. This theorem and its various proofs have”