The Art of Bijective Combinatorics

The art of bijective mathematics: bijective combinatorics course given by Xavier Viennot in four parts (2016-2019) at IMSc, Chenai, India

The Art of Bijective Combinatorics

The art of bijective mathematics: bijective combinatorics course given by Xavier Viennot in four parts (2016-2019) at IMSc, Chenai, India

The maypole braid group

Over the weekend I attended a May Day party thrown by one of my colleagues. During the party they had a traditional maypole dance. An example of a maypole dance is shown at left. A maypole is a tal…

A new lower bound for the Ramsey numbers $R(3,k)$

We prove a new lower bound for the off-diagonal Ramsey numbers, \[ R(3,k) \geq \bigg( \frac{1}{3}+ o(1) \bigg) \frac{k^2}{\log k }\, , \] thereby narrowing the gap between the upper and lower bounds to a factor of $3+o(1)$. This improves the best known lower bound of $(1/4+o(1))k^2/\log k$ due, independently, to Bohman and Keevash, and Fiz Pontiveros, Griffiths and Morris, resulting from their celebrated analysis of the triangle-free process. As a consequence, we disprove a conjecture of Fiz Pontiveros, Griffiths and Morris that the constant $1/4$ is sharp.

Integers 2025 CGT Talks

Combinatorial Game Theory blog. Algorithmic, computational complexity, CGT, abstract games, Nim, Col, Snort, Kayles.

Leave it to Chance. Random Solutions to Deterministic Problems in Discrete Mathematics

Eoin Hurley will defend the dissertation 'Leave it to Chance. Random Solutions to Deterministic Problems in Discrete Mathematics'. Supervisors are Dr J.R. Kang and Prof. M.R.H. Mandjes.

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