Combinatorial optimisation for permutation problems addresses the challenge of arranging discrete elements in an order that minimises or maximises a given objective function. Such problems include the ...

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 structures encompass an array of discrete objects—permutations, set partitions, matchings, trees and lattice paths—whose enumeration and intrinsic properties are often captured by ...

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) ...