Corpus ID: 118004098

# Three tutorial lectures on entropy and counting

@article{Galvin2014ThreeTL,
title={Three tutorial lectures on entropy and counting},
author={David Galvin},
journal={arXiv: Combinatorics},
year={2014}
}
We explain the notion of the {\em entropy} of a discrete random variable, and derive some of its basic properties. We then show through examples how entropy can be useful as a combinatorial enumeration tool. We end with a few open questions.
Entropy-Based Proofs of Combinatorial Results on Bipartite Graphs
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• Computer Science, Mathematics
• 2021 IEEE International Symposium on Information Theory (ISIT)
• 2021
This work considers new entropy-based proofs of some known, or otherwise refined, combinatorial bounds for bipartite graphs. These include upper bounds on the number of the independent sets, lowerExpand
GIBBS MEASURES IN STATISTICAL PHYSICS AND COMBINATORICS (DRAFT)
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• I. Sason
• Mathematics, Computer Science
• ArXiv
• 2020
An information-theoretic proof of Kahn’s conjecture (2001) for a tight upper bound on the number of independent sets in a graph, where this proof applies to bipartite graphs that are regular on one side (the other side may be irregular). Expand
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The present paper provides an information-theoretic proof of Kahn’s conjecture (2001) for a tight upper bound on the number of independent sets in irregular graphs. This conjecture has been recentlyExpand
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Using the Tsallis–Havrda–Charvát type, several results connected with Shearer’s lemma are derived, including upper bounds on the maximum possible cardinality of a family of k-subsets, when no pairwise intersections of these subsets may coincide. Expand
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Problems in extremal graphs and poset theory
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii CHAPTER
Extremal and probabilistic results for regular graphs
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• Mathematics, Computer Science
• ArXiv
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We introduce and study analogues of expander and hyperfinite graph sequences in the context of directed acyclic graphs, which we call "extender" and "hypershallow" graph sequences, respectively. OurExpand

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