Combinatorics and discrete mathematics form a vibrant and expansive branch of modern mathematics, dedicated to the study of finite or countable structures and the methods used to count, classify, and ...

Rushil Mathur, a three-time Indian National Mathematical Olympiad awardee, authored "An Exploration of Olympiad Combinatorics" and will represent India at the International Mathematical Olympiad (IMO) ...

After previously discussing permutations, Dr. James McCaffrey of Microsoft Research uses step-by-step examples and full code presentations to explore combinations. A zero-based mathematical (n, k) ...

Consider this sequence of numbers: 5, 7, 9. Can you spot the pattern? Here’s another with the same pattern: 15, 19, 23. One more: 232, 235, 238. “Three equally spaced things,” says Raghu Meka, a ...

Eric Swartz: application of group theory to finite structures, such as graphs and finite geometries, and problems related to the combinatorics of finite groups.

The mathematician Ben Green of the University of Oxford has made a major stride toward understanding a nearly 100-year-old combinatorics problem, showing that a well-known recent conjecture is “not ...

Mathematical truths are often born of the conflict between order and disorder. Mathematicians discover patterns, and, to better understand the mysterious forces at play, they look for countervailing ...