Two-Sided Eulerian Numbers via Balls in Boxes
By Kyle Petersen. 2012
48 citations recorded by the source corpus.
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.
Subfields: Algebra and Number Theory, Artificial Intelligence, Discrete Mathematics and Combinatorics
View Paper: https://www.semanticscholar.org/paper/68fc517609ab0d8b82cfbdfbc2f4f2b2f0c57895
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In Algebra and Number Theory
In Artificial Intelligence
In Discrete Mathematics and Combinatorics
Citations in the corpus
- Unimodality, log-concavity, real-rootedness and beyond (2015, background): “-CONCAVITY AND REAL{ROOTEDNESS 9 Gessel [53] has conjectured a fascinating property which resembles -nonnegativity for the joint distribution of descents and inverse descents: Conjecture 3.5 (Gessel, [18, 53, 78]). If nis a positive integer, then there are nonnegative numbers c n(k;j) for all k;j2N ”