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628  Articles
1 of 64 pages  |  10  records  |  more records»
In this paper, we present grammatical descriptions of several polynomials associated with Eulerian polynomials, including q-Eulerian polynomials, alternating run polynomials and derangement polynomials. As applications, we get several convolution formulas... see more

We prove various formulas which express exponential generating functions counting permutations by the peak number, valley number, double ascent number, and double descent number statistics in terms of the exponential generating function for Chebyshev poly... see more

We prove various formulas which express exponential generating functions counting permutations by the peak number, valley number, double ascent number, and double descent number statistics in terms of the exponential generating function for Chebyshev poly... see more

In this paper we study the cycle descent statistic on permutations. Several involutions on permutations and derangements are constructed. Moreover, we construct a bijection between negative cycle descent permutations and Callan perfect matchings.

In this paper we study the cycle descent statistic on permutations. Several involutions on permutations and derangements are constructed. Moreover, we construct a bijection between negative cycle descent permutations and Callan perfect matchings.

Using the combinatorial formula for the transformed Macdonald polynomials of Haglund, Haiman, and Loehr, we investigate the combinatorics of the symmetry relation ˜Hµ(x;q,t)=˜Hµ*(x;t,q)\widetilde{H}_\mu(\mathbf{x};q,t)=\widetilde{H}_{\mu^\ast}(\mathbf{x};... see more

In this paper, we introduce a parametric type of Bernoulli polynomials with higher level and study their characteristic and combinatorial properties. We also give determinant expressions of a parametric type of Bernoulli polynomials with higher level. The... see more

We continue our study on relationships between Bernoulli polynomials and balancing (Lucas-balancing) polynomials. From these polynomial relations, we deduce new combinatorial identities with Fibonacci (Lucas) and Bernoulli numbers. Moreover, we prove a sp... see more

The monomiality principle was introduced by G. Dattoli, in order to derive the properties of special or generalized polynomials starting from the corresponding ones of monomials. In this article we show a general technique to extend themonomiality approac... see more

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