Related papers: Partition-theoretic interpretation for certain tru…
We give generalizations of a finite version of Euler's pentagonal number theorem and of a q-identity of Gauss.
In this paper, we give a purely bijective proof that two different partition classes that are both combinatorial interpretations of the partition function $p_\nu(n)$, a partition function related to the third order mock theta function…
We look for partition theorems for large subtrees for suitable uncountable trees and colourings. We concentrate on sub-trees of $^{\kappa \ge} 2$ expanded by a well ordering of each level. Unlike earlier works, we do not ask the embedding…
The probabilistic satisfiability of a logical expression is a fundamental concept known as the partition function in statistical physics and field theory, an evaluation of a related graph's Tutte polynomial in mathematics, and the…
The new interpretation of Quantum Mechanics is based on a complex probability theory. An interpretation postulate specifies events which can be observed and it follows that the complex probability of such event is, in fact, a real positive…
I use an instrumental approach to investigate some commonly made claims about interpretations of quantum mechanics, especially those that pertain questions of locality. The here presented investigation builds on a recently proposed taxonomy…
We exploit transformations relating generalized $q$-series, infinite products, sums over integer partitions, and continued fractions, to find partition-theoretic formulas to compute the values of constants such as $\pi$, and to connect sums…
In this paper, we define Gaussian generalized Tetranacci numbers and as special cases, we investigate Gaussian Tetranacci and Gaussian Tetranacci-Lucas numbers with their properties.
We compute a minimum degree threshold sufficient for 3-partite graphs to admit a fractional triangle decomposition. Together with recent work of Barber, K\"uhn, Lo, Osthus and Taylor, this leads to bounds for exact decompositions and in…
Consider the following truncated Freud linear functional $\mathbf{u}_z$ depending on a parameter $z$, $$\langle\mathbf{u}_z,p\rangle=\int_0^\infty p(x)e^{-zx^4}dx,\quad z>0.$$ The aim of this work is to analyze the properties of the…
Weight-equitable partitions of graphs, which are a natural extension of the well-known equitable partitions, have been shown to be a powerful tool to weaken the regularity assumption in several well-known eigenvalue bounds. In this work we…
We define "splitting functions of level l" for any integer l>0. These functions generalize Dwork's splitting functions : they allow us to represent additive characters of order $p^l$. Then we use these functions to obtain a Stickleberger…
We consider the estimation of quadratic functionals in a Gaussian sequence model where the eigenvalues are supposed to be unknown and accessible through noisy observations only. Imposing smoothness assumptions both on the signal and the…
A mathematical method for constructing fractal curves and surfaces, termed the $p\lambda n$ fractal decomposition, is presented. It allows any function to be split into a finite set of fractal discontinuous functions whose sum is equal…
Schmidt's theorem is significantly generalized, to partitions in which periodic but otherwise arbitrary subsets of parts are counted or uncounted. The identification of such sets of partitions with colored partitions satisfying certain…
Consider the representation of a rational number as a continued fraction, associated with "odd" Euclidean algorithm. In this paper we prove certain properties for the limit distribution function for sequences of rationals with bounded sum…
Within framework of the quantum calculus, we represent the partition function and the mass exponent of a multifractal, as well as the average of random variables distributed over self-similar set, on the basis of the deformed expansion in…
We establish an alternative, ``perpendicular" collection of generating functions for the coefficients of Gaussian polynomials, $\begin{bmatrix}N+m\\m\end{bmatrix}_q$. We provide a general characterization of these perpendicular generating…
The quantale of distance distributions is of fundamental importance for understanding probabilistic metric spaces as enriched categories. Motivated by the categorical interpretation of partial metric spaces, we are led to investigate the…
We investigate the structure of the higher genus topological string amplitudes on the quintic hypersurface. It is shown that the partition functions of the higher genus than one can be expressed as polynomials of five generators. We also…