The boundary of the Eulerian number triangle
Probability
2007-05-23 v1 Combinatorics
Abstract
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.
Cite
@article{arxiv.math/0602610,
title = {The boundary of the Eulerian number triangle},
author = {Alexander Gnedin and Grigori Olshanski},
journal= {arXiv preprint arXiv:math/0602610},
year = {2007}
}
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21 pages