Eulerian polynomials have long occupied a central role in combinatorics, encapsulating critical information about permutation statistics. In their classical formulation, these polynomials encode the ...

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.

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 ...