منابع مشابه
The signed Eulerian numbers on involutions
We de ne an analog of signed Eulerian numbers fn,k for involutions of the symmetric group and derive some combinatorial properties of this sequence. In particular, we exhibit both an explicit formula and a recurrence for fn,k arising from the properties of its generating function.
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We introduce color-signed permutations to obtain a very explicit combinatorial interpretation of the q-Eulerian identities of Brenti and some generalizations. In particular, we prove an identity involving the golden ratio, which allows us to compute upper bounds on how high a checker can reach in a classical checkerjumping problem, when the rules are relaxed to allow also diagonal jumps.
متن کاملA Colorful Involution for the Generating Function for Signed Stirling Numbers of the First Kind
We show how the generating function for signed Stirling numbers of the first kind can be proved using the involution principle and a natural combinatorial interpretation based on cycle-colored permuations. We seek an involution-based proof of the generating function for signed Stirling numbers of the first kind, written here as ∑ k (−1)c(n, k)x = (−1)(x)(x− 1) · · · (x− n+ 1) where c(n, k) is t...
متن کاملCrossings of signed permutations and q-Eulerian numbers of type B
In this paper we want to study combinatorics of the type B permutations and in particular the join statistics crossings, excedances and the number of negative entries. We generalize most of the results known for type A (i.e. zero negative entries) and use a mix of enumerative, algebraic and bijective techniques. This work has been motivated by permutation tableaux of type B introduced by Lam an...
متن کاملDerivatives 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...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1992
ISSN: 0012-365X
DOI: 10.1016/0012-365x(92)90365-m