Related papers: Disturbing the $q$-Dyson Conjecture

We collect here various conjectures on congruences made by the author in a series of papers, some of which involve binary quadratic forms and other advanced theories. Part A consists of 100 unsolved conjectures of the author while…

In this paper, we formulate and prove several variants of the Erd\H{o}s-Tur\'{a}n additive bases conjecture.

We give a formal Laurent series proof of Andrews's $q$-Dyson Conjecture, first proved by Zeilberger and Bressoud.

We give a survey of some known and some new results about factors of different sorts of $q-$Fibonacci numbers.

We consider the extension of the Jackson calculus into higher dimensions and specifically into Clifford analysis.

By extending Lv-Xin-Zhou's first layer formulas of the $q$-Dyson product, we prove Kadell's conjecture for the Dyson product and show the error of his $q$-analogous conjecture. With the extended formulas we establish a $q$-analog of…

Variants of the q-hypergeometric equation were introduced in our previous paper with Hatano. In this paper, we consider degenerations of the variant of the q-hypergeometric equation, which is a q-analogue of confluence of singularities in…

The review of modern study of algebraic, geometric and differential properties of quaternionic (Q) numbers with their applications. Traditional and "tensor" formulation of Q-units with their possible representations are discussed and groups…

In this note we outline the history of q-deformations; indicate their physical shortcomings; suggest their apparent resolution via an invariant formulation based on a new mathematics of genotopic type; and point out their expected physical…

In this paper we introduce the notion of $e$-computability as a method of finding the Waring rank of forms. We use this notion to find infinitely many new examples which satisfy Strassen's Conjecture.

We give a counterexample to a recently conjectured variant of the Penrose inequality.

We give a proof of a recent combinatorial conjecture due to the first author, which was discovered in the framework of commutative algebra. This result gives rise to new companions to the famous Andrews-Gordon identities. Our tools involve…

We describe an algorithm that computes possible corners of hypothetical counterexamples to the Jacobian Conjecture up to a given bound. Using this algorithm we compute the possible families corresponding to $\gcd(deg(P),deg(Q))\le 35$, and…

We prove generalized versions of some conjectures of Joel Lewis on the number of alternating permutations avoiding certain patterns. Our main tool is the perhaps surprising observation that a classic bijection on pattern avoiding…

A possible scheme of q-deformation, which was recently developed by the present authors, is reviewed by stressing the starting idea.

This is a collection of variants of Schanuel's conjecture and the known dependencies between them. It was originally written in 2007, and made available for a time on my webpage. I have been asked by a few people to make it available again…

In this paper we state some conjectures about q-Fibonacci polynomials which for q=1 reduce to well-known results about Fibonacci numbers and Fibonacci polynomials.

Let $p$ be an odd prime. In the paper we collect the author's various conjectures on congruences modulo $p$ or $p^2$, which are concerned with sums of binomial coefficients, Lucas sequences, power residues and special binary quadratic…

I settle a conjecture of Andrews related to the Alladi-Schur polynomials. In addition, I give further relations and implications to two families of polynomials related to the Alladi-Schur polynomials.

An algebraic method is used to study the semantics of exceptions in computer languages. The exceptions form a computational effect, in the sense that there is an apparent mismatch between the syntax of exceptions and their intended…