Cumulants and convolutions via Abel polynomials
نویسندگان
چکیده
منابع مشابه
Linear Recurrence Sequences and Their Convolutions via Bell Polynomials
We recast homogeneous linear recurrence sequences with fixed coefficients in terms of partial Bell polynomials, and use their properties to obtain various combinatorial identities and multifold convolution formulas. Our approach relies on a basis of sequences that can be obtained as the INVERT transform of the coefficients of the given recurrence relation. For such a basis sequence with generat...
متن کاملJack polynomials and free cumulants
We study the coefficients in the expansion of Jack polynomials in terms of power sums. We express them as polynomials in the free cumulants of the transition measure of an anisotropic Young diagram. We conjecture that such polynomials have nonnegative integer coefficients. This extends recent results about normalized characters of the symmetric group. 2000 Mathematics Subject Classification: 05...
متن کاملOn Abel-Gontscharoff-Gould's polynomials
In this paper a connective study of Gould’s annihilation coefficients and Abel-Gontscharoff polynomials is presented. It is shown that Gould’s annihilation coefficients and Abel-Gontscharoff polynomials are actually equivalent to each other under certain linear substitutions for the variables. Moreover, a pair of related expansion formulas involving Gontscharoff’s remainder and a new form of it...
متن کاملMultivariate Delta Gon£arov and Abel Polynomials
Classical Gon£arov polynomials are polynomials which interpolate derivatives. Delta Gon£arov polynomials are polynomials which interpolate delta operators, e.g., forward and backward difference operators. We extend fundamental aspects of the theory of classical bivariate Gon£arov polynomials and univariate delta Gon£arov polynomials to the multivariate setting using umbral calculus. After intro...
متن کاملCumulants of the q-semicircular law, Tutte polynomials, and heaps
The q-semicircular distribution is a probability law that interpolates between the Gaussian law and the semicircular law. There is a combinatorial interpretation of its moments in terms of matchings where q follows the number of crossings, whereas for the free cumulants one has to restrict the enumeration to connected matchings. The purpose of this article is to describe combinatorial propertie...
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: European Journal of Combinatorics
سال: 2010
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2010.03.002