A new proof from the Australian science fiction writer Greg Egan and a 2011 proof anonymously posted online are now being hailed as significant advances on a puzzle mathematicians have been studying ...

Combinatorial enumeration and pattern avoidance represent a vibrant area of modern discrete mathematics, where the objective is to count and characterise structures subject to specific constraints.

Combinatorial designs and finite group theory form a rich intersection of discrete mathematics and algebra, where structured arrangements of elements are studied alongside the algebraic properties of ...

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) ...