Generalized Eulerian Numbers
نویسندگان
چکیده
منابع مشابه
Derivatives and Eulerian Numbers
The aim of the present note is to give a closed form formula for the nth derivative of a function which satisfies Riccati’s differential equation with constant coefficients. The paper is organized as follows. In section 2 we recall the definition and basic properties of Eulerian numbers. We introduce and prove the mentioned formula in section 3. Some examples where the formula can be applied ar...
متن کاملEulerian-Catalan Numbers
We show that the Eulerian-Catalan numbers enumerate Dyck permutations. We provide two proofs for this fact, the first using the geometry of alcoved polytopes and the second a direct combinatorial proof via an Eulerian-Catalan analogue of the Chung-Feller theorem.
متن کاملCongruences on Stirling Numbers and Eulerian Numbers
In this paper, we establish some Fleck-Weisman type congruences for the Stirling numbers and the Eulerian numbers.
متن کاملLaurent polynomials and Eulerian numbers
Article history: Received 24 August 2009 Available online 25 February 2010
متن کاملGeneralized 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...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Advances in Pure Mathematics
سال: 2018
ISSN: 2160-0368,2160-0384
DOI: 10.4236/apm.2018.83018