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Enumerative Combinatorics
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The article was published on 1997-04-13 and is currently open access. It has received 7046 citations till now. The article focuses on the topics: Enumerative combinatorics & Algebraic combinatorics.read more
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Journal Article
The On-Line Encyclopedia of Integer Sequences.
TL;DR: The On-Line Encyclopedia of Integer Sequences (OEIS) as mentioned in this paper is a database of 13,000 number sequences and is freely available on the Web (http://www.att.com/~njas/sequences/) and is widely used.
Book
Graphical Models, Exponential Families, and Variational Inference
TL;DR: The variational approach provides a complementary alternative to Markov chain Monte Carlo as a general source of approximation methods for inference in large-scale statistical models.
Book ChapterDOI
The On-Line Encyclopedia of Integer Sequences
TL;DR: The On-Line Encyclopedia of Integer Sequences (or OEIS) is a database of some 130000 number sequences which serves as a dictionary, to tell the user what is known about a particular sequence and is widely used.
Journal ArticleDOI
Constructing free-energy approximations and generalized belief propagation algorithms
TL;DR: This work explains how to obtain region-based free energy approximations that improve the Bethe approximation, and corresponding generalized belief propagation (GBP) algorithms, and describes empirical results showing that GBP can significantly outperform BP.
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Comparing clusterings---an information based distance
TL;DR: This paper proposes an information theoretic criterion for comparing two partitions, or clusterings, of the same data set, called variation of information (VI), and presents it from an axiomatic point of view, showing that it is the only ''sensible'' criterion for compare partitions that is both aligned to the lattice and convexely additive.
References
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Book
The theory of partitions
TL;DR: The elementary theory of partitions and partitions in combinatorics can be found in this article, where the Hardy-Ramanujan-Rademacher expansion of p(n) is considered.
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The complexity of enumeration and reliability problems
TL;DR: For a large number of natural counting problems for which there was no previous indication of intractability, that they belong to the class of computationally eqivalent counting problems that are at least as difficult as the NP-complete problems.
Book
A history of Greek mathematics
TL;DR: A text which looks at the history of Greek mathematics is presented in this article, a subject on which the author established a special authority by his succession of works on Diophantus, Apolonius of Perga, Archimedes, Euclid and Aristarchus.
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Asymptotic Methods in Enumeration
TL;DR: In this article, a survey of tools used in asymptotic analysis for enumeration problems is presented, focusing on tools which are general, are easily applied, and give estimates of the form $a_n \sim f(n)$.