Related papers: There are no Coincidences
We use the fact that certain cosets of the stabilizer of points are pairwise conjugate in a symmetric group $S_n$ in order to construct recurrence relations for enumerating certain subsets of $S_n$. Occasionally one can find `closed form'…
In this paper a small survey is presented on fourteen sequences, such as: G Add-on Sequences, Sieve Sequences, Digital Sequences, Non-Arithmetic Progressions, recreational sequences (Lucky…
Let $G$ be a graph such that, whenever two vertices $x$ and $y$ of $G$ are joined by three internally disjoint paths, $x$ and $y$ are adjacent. Jamison and Mulder determined that the set of such graphs coincides with the set of graphs that…
We give a new proof of the fact that Barker polynomials of even degree greater than 12, and hence Barker sequences of odd length greater than 13 do not exist. This is intimately tied to irreducibility questions and proved as a consequence…
We prove three conjectures, related to the paperfolding sequence, in a recent paper [arXiv:2005.04066] of P. Barry.
Analogical proportions compare pairs of items (a, b) and (c, d) in terms of their differences and similarities. They play a key role in the formalization of analogical inference. The paper first discusses how to improve analogical inference…
For non-equilibrium systems described by finite Markov processes, we consider the number of times that a system traverses a cyclic sequence of states (a cycle). The joint distribution of the number of forward and backward instances of any…
With the growing importance of detecting misinformation, many studies have focused on verifying factual claims by retrieving evidence. However, canonical fact verification tasks do not apply to catching subtle differences in factually…
Number sequences defined by a linear recursion relation are studied by means of generating functions. Indices of the terms in the recursion relation have arbitrary differenses. In addition to formulas for the nth term an algorithm is…
We study countable graphs that -- up to isomorphism and with probability one -- arise from a random process, in a similar fashion as the Rado graph. Unlike in the classical case, we do not require that probabilities assigned to pairs of…
This paper presents a comparison of the quality of randomness of D sequences based on diehard tests. Since D sequences can model any random sequence, this comparison is of value beyond this specific class.
In [3] we constructed the parity-biquandle bracket valued in {\em pictures} (linear combinations of $4$-valent graphs). We gave no example of classical links such that the parity-biquandle bracket of which is not trivial. In the present…
We study random graph models for directed acyclic graphs, an important class of networks that includes citation networks, food webs, and feed-forward neural networks among others. We propose two specific models, roughly analogous to the…
Suppose you look at today's stock prices and bet on the value of the first digit. One could guess that a fair bet should correspond to the frequency of $1/9 = 11.11%$ for each digit from 1 to 9. This is by no means the case, and one can…
Two series of binary observations $x_1,x_1,...$ and $y_1,y_2,...$ are presented: at each time $n\in\N$ we are given $x_n$ and $y_n$. It is assumed that the sequences are generated independently of each other by two B-processes. We are…
Fibonacci sequence, generated by summing the preceding two terms, is a classical sequence renowned for its elegant properties. In this paper, leveraging properties of generalized Fibonacci sequences and formulas for consecutive sums of…
In the theory of line graphs of undirected graphs there exists an important theorem linking the incidence matrix of the root graph to the adjacency matrix of its line graph. For directed or mixed graphs, however, the exists no analogous…
We complement a recent result of S. Furuichi, by showing that the differences $\sum_{i=1}^n \alpha_i x_i - \prod_{i=1}^n x_i^{\alpha_i}$ associated to distinct sequences of weights are comparable, with constants that depend on the smallest…
We propose some new results on the comparison of the minimum or maximum order statistic from a random number of non-identical random variables. Under the non-identical set-up, with certain conditions, we prove that random minimum (maximum)…
This paper has several objectives. First, it separates randomness from lawlessness and shows why even genuine randomness does not imply lawlessness. Second, it separates the question -why should I call a phenomenon random? (and answers it…