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Two-Sided Eulerian Numbers via Balls in Boxes
T. Kyle Petersen
Vol. 86, No. 3 (June 2013), pp. 159-176
Published by: Mathematical Association of America
Stable URL: http://www.jstor.org/stable/10.4169/math.mag.86.3.159
Page Count: 18
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Summary The Eulerian numbers count permutations according to the number of descents. The two-sided Eulerian numbers count permutations according to number of descents and the number of descents in the inverse permutation. Here we derive some results for Eulerian and two-sided Eulerian numbers using an elementary “balls-in-boxes” approach. We also discuss an open conjecture of Ira Gessel about the two-sided Eulerian numbers.
Copyright the Mathematical Association of America 2013