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Symmetric identity for polynomial sequences satisfying A n + 1 ' ( x ) = ( n + 1 ) A n ( x )

Farid Bencherif, Rachid Boumahdi, Tarek Garici (2021)

Communications in Mathematics

Using umbral calculus, we establish a symmetric identity for any sequence of polynomials satisfying A n + 1 ' ( x ) = ( n + 1 ) A n ( x ) with A 0 ( x ) a constant polynomial. This identity allows us to obtain in a simple way some known relations involving Apostol-Bernoulli polynomials, ApostolEuler polynomials and generalized Bernoulli polynomials attached to a primitive Dirichlet character.

Symmetric partitions and pairings

Ferenc Oravecz (2000)

Colloquium Mathematicae

The lattice of partitions and the sublattice of non-crossing partitions of a finite set are important objects in combinatorics. In this paper another sublattice of the partitions is investigated, which is formed by the symmetric partitions. The measure whose nth moment is given by the number of non-crossing symmetric partitions of n elements is determined explicitly to be the "symmetric" analogue of the free Poisson law.

Symmetries of random discrete copulas

Arturo Erdely, José M. González–Barrios, Roger B. Nelsen (2008)

Kybernetika

In this paper we analyze some properties of the discrete copulas in terms of permutations. We observe the connection between discrete copulas and the empirical copulas, and then we analyze a statistic that indicates when the discrete copula is symmetric and obtain its main statistical properties under independence. The results obtained are useful in designing a nonparametric test for symmetry of copulas.

Systèmes aux q -différences singuliers réguliers : classification, matrice de connexion et monodromie

Jacques Sauloy (2000)

Annales de l'institut Fourier

G.D. Birkhoff a posé, par analogie avec le cas classique des équations différentielles, le problème de Riemann-Hilbert pour les systèmes “fuchsiens” aux q -différences linéaires, à coefficients rationnels. Il l’a résolu dans le cas générique: l’objet classifiant qu’il introduit est constitué de la matrice de connexion P et des exposants en 0 et . Nous reprenons sa méthode dans le cas général, mais en traitant symétriquement 0 et et sans recours à des solutions à croissance “sauvage”. Lorsque q ...

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