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We give an elementary development of a complete asymptotic expansion for the Catalan-Larcombe-French sequence.

Ramsey theory is a highly active research area in mathematics that studies the emergence of order in large disordered structures. Ramsey numbers mark the threshold at which order first appears and are extremely difficult to calculate due to their explosive rate of growth. Recently, an algorithm that can be implemented using adiabatic quantum evolution has… (More)

In the Graph Isomorphism (GI) problem two N-vertex graphs G and G are given and the task is to determine whether there exists a permutation of the vertices of G that preserves adjacency and transforms G → G. If yes, then G and G are said to be isomorphic; otherwise they are non-isomorphic. The GI problem is an important problem in computer science and is… (More)

We prove a two-point concentration for the independent domination number of the random graph G n,p provided p 2 ln(n) ≥ 64ln((ln n)/p).

- Lane Clark
- 2002

We give central and local limit theorems for the number of excedances of a uniformly distributed random permutation belonging to certain sequences of conjugacy classes and belonging to the sequence of derangements.

- Graeme Smith, John Smolin, Zhengbing Bian, Fabian Chudak, William G Macready, Lane Clark +1 other
- 2013

A machine consisting of nearly 100 quantum circuit elements can compute the solution to a classic problem in mathematics, but is it a quantum computer? What is a quantum computer? We could say it's a machine that calculates solutions to problems using quantum components. But this definition is incomplete; after all, an abacus is made of quantum elements… (More)

- Lane Clark, Sarah Holliday, John Mcsorley, Thomas Porter, Clark, Sarah +4 others
- 2016

Properties of (connected) graphs whose closed or open neighborhood families are Sperner, anti-Sperner, distinct or none of the proceeding have been extensively examined. In this paper we examine 24 properties of the neighborhood family of a graph. We give asymptotic formulas for the number of (connected) labelled graphs for 12 of these properties. For the… (More)