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We show that essentially the Fibonacci sequence is the unique binary recurrence which contains infinitely many three-term arithmetic progressions. A criterion for general linear recurrences having infinitely many three-term arithmetic…
A method for encoding and decoding spectrum shaped binary run-length constrained sequences is described. The binary sequences with predefined range of exponential sums are introduced. On the base of Cover's enumerative scheme, recurrence…
Double triangle expansion is an operation on $4$-regular graphs with at least one triangle which replaces a triangle with two triangles in a particular way. We study the class of graphs which can be obtained by repeated double triangle…
The Fibonacci sequence is obtained as weighted sum along the rows in the Pascal triangle by choosing a periodic up-and-down pattern of weights from the set $\{-1,-\frac{1}{2},0, \frac{1}{2}, 1\}$. A graphical illustration of this identity…
Multi-edge networks capture repeated interactions between individuals. In social networks, such edges often form closed triangles, or triads. Standard approaches to measure this triadic closure, however, fail for multi-edge networks,…
This paper is an attempt to apply the tools of supergeometry to arithmetic. Supergeometric objects are defined over supercommutative rings of coefficients, and we consider an integral ring with exactly two odd variables. In this case the…
The notion of a two-dimensional word arises naturally in the study of combinatorics on words, while the iterative construction of pedal triangles results in a rich dynamical system in the study of geometry. At first, these two classes of…
Stereo vision is an effective technique for depth estimation with broad applicability in autonomous urban and highway driving. While various deep learning-based approaches have been developed for stereo, the input data from a binocular…
We propose new algorithms for computing triangular decompositions of polynomial systems incrementally. With respect to previous works, our improvements are based on a {\em weakened} notion of a polynomial GCD modulo a regular chain, which…
Persistent homology, a technique from computational topology, has recently shown strong empirical performance in the context of graph classification. Being able to capture long range graph properties via higher-order topological features,…
Extended persistence is a technique from topological data analysis to obtain global multiscale topological information from a graph. This includes information about connected components and cycles that are captured by the so-called…
We consider the geometric generalization of ordinary continued fraction to the multidimensional case introduced by F. Klein in 1895. A multidimensional periodic continued fraction is the union of sails with some special group acting freely…
Strict partitions are enumerated with respect to the weight, the number of parts, and the number of sequences of odd length. We write this trivariate generating function as a double sum $q$-series. Equipped with such a combinatorial set-up,…
Duplicate removal is a critical step to accomplish a reasonable amount of predictions in prevalent proposal-based object detection frameworks. Albeit simple and effective, most previous algorithms utilize a greedy process without making…
A common method to define a parallel solution for a computational problem consists in finding a way to use the Divide and Conquer paradigm in order to have processors acting on its own data and scheduled in a parallel fashion. MapReduce is…
Persistent Topology studies topological features of shapes by analyzing the lower level sets of suitable functions, called filtering functions, and encoding the arising information in a parameterized version of the Betti numbers, i.e. the…
Folding a sequence $S$ into a multidimensional box is a method that is used to construct multidimensional codes. The well known operation of folding is generalized in a way that the sequence $S$ can be folded into various shapes. The new…
We describe various properties of continued fraction expansions of complex numbers in terms of Gaussian integers. Numerous distinct such expansions are possible for a complex number. They can be arrived at through various algorithms, as…
The paper deals with the problem of reconstructing the topological structure of a network of dynamical systems. A distance function is defined in order to evaluate the "closeness" of two processes and a few useful mathematical properties…
Take a multiplicative monoid of sequences in which the multiplication is given by Hadamard product. The set of linear combinations of interleaving monoid elements then yields a ring. For hypergeometric sequences, the resulting ring is a…