A. Vishnyakova

activity

20242026

collaborators

6 papers

math.CV2026

Polynomially Deformed Normalized Pochhammer Sequences Having Generating Functions With Only Real Non-positive Zeros

Anna Vishnyakova

For a given real number $a > 0$ and a given real polynomial $P_{n} \in R [x]$ of degree $n = 0, 1, 2, \dots$ it is easy to see that $ \sum_{k=0}^\infty \frac{(a)_k}{k!} P_n(k) z^…

math.CV2026

Polynomials interpolated totally positive sequences

Anna Vishnyakova

A real sequence $(a_{k})_{k = 0}^{\infty}$ is called {\it totally positive} if all minors of the infinite Toeplitz matrix $∥ a_{j - i} ∥_{i, j = 0}^{\infty}$ are nonnegative (wh…

math.CV2025

Convolution operators preserving the set of totally positive sequences

Olga Katkova, Anna Vishnyakova

A real sequence $(a_{k})_{k = 0}^{\infty}$ is called {\it totally positive} if all minors of the infinite Toeplitz matrix $∥ a_{j - i} ∥_{i, j = 0}^{\infty}$ are nonnegative (he…

math.CO2025

Generalized $f$ -Eulerian polynomials: zeros and hypergeometric representations with applications

Dmitrii Karp, Anna Vishnyakova

In this paper, we explore (slightly generalized) $f$ -Eulerian polynomials introduced by Stanley and frequently appearing in combinatorics. Notable special cases include the classic…

math.CA2025

Unimodality preservation by ratios of functional series and integral transforms

Dmitrii Karp, Anna Vishnyakova, Yi Zhang

An elementary, but very useful lemma due to Biernacki and KrzyÅ¼ (1955) asserts that the ratio of two power series inherits monotonicity from that of the sequence of ratios of thei…

math.CV2024

On the number of real zeroes of a homogeneous differential polynomial and a generalization of the Hawaii conjecture

Olga Katkova, Mikhail Tyaglov, Anna Vishnyakova

For a given real polynomial $p$ we study the possible number of real roots of a differential polynomial $H_{\varkappa}[p](x) = \varkappa\left(p'(x)\right)^2-p(x)p''(x), \varkappa \…