Related papers: Disturbing the $q$-Dyson Conjecture
New cases of the multiplicity conjecture are considered.
Using $q$-series identities and series rearrangement, we establish several extensions of $q$-Watson formulas with two extra integer parameters. Then they and Sears' transformation formula are utilized to derive some generalizations of…
A new representation of Dirac's delta-distribution, based on the so-called q-exponentials, has been recently conjectured. We prove here that this conjecture is indeed valid.
The content of this work is concerned with Jordan-Schwinger calculus using $q$-deformed bosons.
In this paper we investigate some interesting formulae of q-Euler numbers and polynomials related to the modified q-Bernstein polynomials.
Using algebraic transformations and equivalent reformulations we derive a number of new results from some earlier ones (by the author) in more accepted terms closely related to well-known conjectures of Bondy and Jung including a number of…
This essay considers ways that recent uses of computers in mathematics challenge contemporary views on the nature of mathematical understanding. It also puts these challenges in a historical perspective and offers speculation as to a…
An alternative computational approach to the Collatz (3n+1) conjecture is presented that may be theoretically capable of confirming the conjecture.
A particular case of the Jacobian conjecture is considered and for small dimensional cases a computational approach is offered
Using a general $q$-series expansion, we derive some nontrivial $q$-formulas involving many infinite products. A multitude of Hecke--type series identities are derived. Some general formulas for sums of any number of squares are given. A…
Up-down permutations are counted by tangent resp. secant numbers. Considering words instead, where the letters are produced by independent geometric distributions, there are several ways of introducing this concept; in the limit they all…
We formulate and discuss two conjectures concerning recursive formulae for Branson's $Q$-curvatures. The proposed formulae describe all $Q$-curvatures on manifolds of all even dimensions in terms of respective lower order $Q$-curvatures and…
In this paper we shall evaluate two alternating sums of binomial coefficients by a combinatorial argument. Moreover, by combining the same combinatorial idea with partition theoretic techniques, we provide $q$-analogues involving the…
One presents many Concatenated and Operation Sequences, P-Q Relationships, Digital Sequences, Magic Squares, Prime Conjectures, k-Divisibility and Strong Divisibility Sequences, Geometric Conjectures, Proposed problems.
We provide a proof of a variant of the Landau-Siegel Zeros conjecture.
In this short note we report on results on a computational search for a counterexample to the strong coincidence conjecture. In particular, we discuss the method used so that further searches can be conducted.
In this paper we study the variation diminishing kernel as a part of the $q$-calculus. We introduce the $q$-Macdonald function a newborne in the family of the $q$-special functions which play a central role in this study.
This paper describes a method used to construct infinitely many probable counterexamples of the abc conjecture over the rational integers.
Several conjectural continued fractions found with the help of various algorithms are published in this paper.
We introduce a new method in the attempt to prove the Jacobian conjecture. In the complex dimension 2 case, we apply this method to prove some new results related the Jacobian conjecture.