منابع مشابه
Generalized Eulerian sums
In this note, we derive a number of symmetrical sums involving Eulerian numbers and some of their generalizations. These extend earlier identities of Don Knuth and the authors, and also include several q-nomial sums inspired by recent work of Shareshian and Wachs on the joint distribution of various permutation statistics, such as the number of excedances, the major index and the number of fixe...
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The (q, r)-Eulerian polynomials are the (maj−exc, fix, exc) enumerative polynomials of permutations. Using Shareshian and Wachs’ exponential generating function of these Eulerian polynomials, Chung and Graham proved two symmetrical q-Eulerian identities and asked for bijective proofs. We provide such proofs using Foata and Han’s three-variable statistic (inv−lec, pix, lec). We also prove a new ...
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ژورنال
عنوان ژورنال: Journal of Combinatorics
سال: 2012
ISSN: 2156-3527,2150-959X
DOI: 10.4310/joc.2012.v3.n3.a3