The boundary of the Eulerian number triangle

Details The boundary of the Eulerian number triangle The boundary of the Eulerian number triangle

2006-02-27

arxiv.org/abs/math/0602610v1

Moscow Mathematical Journal 6 (2006), no 3, 461-475

Mathematics

Probability

21 pages

Scientific paper

The 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.

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