# 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.

#### 41 Citations

Entropy-Based Proofs of Combinatorial Results on Bipartite Graphs

- 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, lower… Expand

GIBBS MEASURES IN STATISTICAL PHYSICS AND COMBINATORICS (DRAFT)

- 2018

These are notes for lectures on Gibbs measures in statistical physics and combinatorics presented in Athens, Greece, May 2017, as part of the ‘Techniques in Random Discrete Structures’ summer school.

An Information-Theoretic Proof of a Bound on the Number of Independent Sets in Bipartite Graphs

- 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

An Information-Theoretic Proof of a Tight Bound on the Number of Independent Sets in Graphs

- 2020

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 recently… Expand

Notes on use of Generalized Entropies in Counting

- Mathematics, Computer Science
- Graphs Comb.
- 2016

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

Structure and randomness in extremal combinatorics

- Mathematics
- 2017

In this thesis we prove several results in extremal combinatorics from areas including Ramsey theory, random graphs and graph saturation. We give a random graph analogue of the classical Andr´asfai,… Expand

Problems in extremal graphs and poset theory

- Mathematics
- 2018

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Extremal and probabilistic results for regular graphs

- Mathematics
- 2017

In this thesis we explore extremal graph theory, focusing on new methods which apply to different notions of regular graph. The first notion is dregularity, which means each vertex of a graph is… Expand

Chang's lemma via Pinsker's inequality

- Mathematics, Computer Science
- Discret. Math.
- 2020

A short information theoretic proof for Chang’s lemma that is based on Pinsker's inequality is given and it is shown that Chang's lemma is correct on both sides of the inequality. Expand

On directed analogues of expander and hyperfinite graph sequences

- Mathematics, Computer Science
- ArXiv
- 2020

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. Our… Expand

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