2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/120645The Eulerian triangle is a classical array of combinatorial numbers defined by a linear recursion. The associated boundary problem asks one to find all extreme nonnegative solutions to a dual recursion. Exploiting connections with random permutations and Markov chains we show that the boundary is discrete and explicitly identify its elements.21 pagesProbabilityCombinatorics60J50; 60C05text