Related papers: A note on number triangles that are almost their o…
Productions functions map the inputs of a firm or a productive system onto its outputs. This article expounds generalizations of the production function that include state variables, organizational structures and increasing returns to…
We investigate the coefficients generated by expressing the falling factorial $(xy)_k$ as a linear combination of falling factorial products $(x)_l (y)_m$ for $l,m =1,...,k$. Algebraic and combinatoric properties of these coefficients are…
We attach a ring of sequences to each number from a certain class of extremal real numbers, and we study the properties of this ring both from an analytic point of view by exhibiting elements with specific behaviors, and also from an…
The cyclic group labeled family of quasi-projection operators is used for investigation of decomposition of functions with respect to the cyclic group of order n . Series of new identities thus arising are demonstrated and new perspectives…
Divisibility sequences are defined by the property that their elements divide each other whenever their indices do. The divisibility sequences that also satisfy a linear recurrence, like the Fibonacci numbers, are generated by polynomials…
By investigating a recurrence relation about functions, we first give alternative proofs of various identities on Fibonacci numbers and Lucas numbers, and then, make certain well known identities visible via certain trivalent graph…
A new family of asymmetric matrices of Walsh-Hadamard type is introduced. We study their properties and, in particular, compute their determinants and discuss their eigenvalues. The invertibility of these matrices implies that certain…
Rectangulations are partitions of a square into axis-aligned rectangles. A number of results provide bijections between combinatorial equivalence classes of rectangulations and families of pattern-avoiding permutations. Other results deal…
Our focus is on the set of lower-triangular, infinite matrices that have natural operations like addition, multiplication by a number, and matrix multiplication. With respect to addition this set forms and abelian group while with respect…
A simple graph is called triangular if every edge of it belongs to a triangle. We conjecture that any graphical degree sequence all terms of which are greater than or equal to 4 has a triangular realisation, and establish this conjecture…
Graphs are used in many disciplines to model the relationships that exist between objects in a complex discrete system. Researchers may wish to compare a network of interest to a "typical" graph from a family (or ensemble) of graphs which…
Some natural proteins display recurrent structural patterns. Despite being highly similar at the tertiary structure level, repetitions within a single repeat protein can be extremely variable at the sequence level. We propose a mathematical…
For a family of polytopes of even dimension $2p$, known as \textit{dual-neighborly}, it has been shown for $p\ne 2$ that the associated intersection of quadrics is a connected sum of sphere products $S^p\times S^p$. In this article we give…
A dual approach to defining the triangle sequence (a type of multidimensional continued fraction algorithm, initially developed in NT/9906016) for a pair of real numbers is presented, providing a new, clean geometric interpretation of the…
Let $ \prod_{i=1}^d (X-\alpha_i Y) \in{\mathbb C}[X,Y]$ be a binary form and let $\epsilon_1,\dots,\epsilon_d$ be nonzero complex numbers. We consider the family of binary forms $ \prod_{i=1}^d (X-\alpha_i \epsilon_i^aY)$, $a\in {\mathbb…
A triangular field of rational numbers is characterized, with relations to Stirling numbers 2nd, Hyperbolic functions, and centered Binomial distribution. A Generating function is given.
We define and investigate a new three-parameter family of graphs that further generalizes the Fibonacci and metallic cubes. Namely, the number of vertices in this family of graphs satisfies Horadam recurrence, a linear recurrence of second…
In this paper, we study a structured family of matrices whose entries are given by products of $k$-Fibonacci and $k$-Lucas numbers. For this family, we obtain explicit and unified formulas for several classical matrix invariants, including…
This text investigates relations between two well-known family of algorithms, matrix factorisations and recursive linear filters, by describing a probabilistic model in which approximate inference corresponds to a matrix factorisation…
The study of Ramanujan-type congruences for functions specific to additive number theory has a long and rich history. Motivated by recent connections between divisor sums and overpartitions via congruences in arithmetic progressions, we…