Related papers: Disturbing the $q$-Dyson Conjecture
We explore several variations on the recently discovered phenomena of murmurations for elliptic curves and modular forms.
The Donald-Flanigan conjecture asserts that any group algebra of a finite group has a separable deformation. We apply an inductive method to deform group algebras from deformations of normal subgroup algebras, establishing an infinite…
The $q$-Heun equation and its variants arise as degenerations of Ruijsenaars-van Diejen operators with one particle. We investigate local properties of these equations. In particular we characterize the variants of the $q$-Heun equation by…
We study motivic Donaldson-Thomas invariants in the sense of Behrend-Bryan-Szendroi. A wall-crossing formula under a mutation is proved for a certain class of quivers with potentials.
This paper addresses a theory of R(p,q)-deformed combinatorics in discrete probability. It mainly focuses on R(p,q)-deformed factorials, binomial coefficients, Vandermonde's formula, Cauchy's formula, binomial and negative binomial…
We study some conjectures about Chow groups of varieties of geometric genus one. Some examples are given of Calabi-Yau threefolds where these conjectures can be verified, using the theory of finite-dimensional motives.
We put a new conjecture on primes from the point of view of its binary expansions and make a step towards justification.
Understanding neural networks is becoming increasingly important. Over the last few years different types of visualisation and explanation methods have been proposed. However, none of them explicitly considered the behaviour in the presence…
With the increasing deployment of machine learning systems in practice, transparency and explainability have become serious issues. Contrastive explanations are considered to be useful and intuitive, in particular when it comes to…
In this paper we consider carlitz q-Bernoulli numbers and q-stirling numbers of the first and the second kind. From these numbers we derive many interesting formulae associated with q-Bernoulli numbers.
In this article we present a pedagogical introduction of the main ideas and recent advances in the area of topological quantum computation. We give an overview of the concept of anyons and their exotic statistics, present various models…
Let $X$ be a random variable that takes its values in $\frac{1}{q}\mathbb{Z}$, for some integer $q\ge2$, and consider $X$ rounded to an integer, either downwards or upwards or to the nearest integer. We give general formulas for the…
The classical quadratic formula and some of its lesser known variants for solving the quadratic equation are reviewed. Then, a new formula for the roots of a quadratic polynomial is presented.
We study the shifted convolution sums associated to completely multiplicative functions taking values in $\{\pm 1\}$ and give combinatorical proofs of two recent results in the direction of Chowla's conjecture. We also determine the…
This article is part of an ongoing investigation of the two-dimensional Jacobian conjecture. In the first paper of this series, we proved the generalized Magnus' formula. In this paper, inspired by cluster algebras, we introduce a sequence…
This note is devotes to some remarks regarding the use of variational methods, of minimax type, to establish continuity type results
Let $\Phi_{n}(q)$ denote the $n$-th cyclotomic polynomial in $q$. Recently, Guo and Schlosser [Constr. Approx. 53 (2021), 155--200] put forward the following conjecture: for an odd integer $n>1$, \begin{align*}…
In this paper we consider the weighted q-Bernoulli numbers and polynomials which are differnt type of Carlitz's q-Bernoulli numbers and polynomials. From these numbers and polynomials, we derive some interesting formulaes and identities.
In this paper, we survey some recent results on the Artin conjecture and discuss some aspects for the Artin conjecture.
We prove universal recursive formulas for Branson's $Q$-curvatures in terms of respective lower-order $Q$-curvatures, lower-order GJMS-operators and holographic coefficients.