The Art of Discrete and Applied Mathematics (ADAM) is a modern, dynamic, platinum open access, electronic journal that will publish high-quality articles arbitrary length in contemporary discrete applied mathematics which neither the authors nor readers incur any costs.

The Gray configuration is a (27_3) which typically realized as the points and lines of 3 x integer lattice. It occurs member an infinite family configurations defined by Bouwer in 1972. Since their discovery, both its Levi graph (i.e., point-line incidence graph) have been subject intensive study. Its automorphism group contains cyclic subgroups isomorphic to Z_3 Z_9, so it natural ask whether can be plane with any corresponding rotational symmetry. In this paper, we show that there are two...

We call a convex polytope P of dimension 3 admissible if it has the following two properties: (1) for each vertex set its first-neighbours is coplanar; (2) all planes determined by are distinct. It shown that Levi graph point-plane configuration obtained V -construction from an Kronecker cover 1-skeleton . investigate combinatorial nature and use on unit-distance graphs to construct novel isometric point-circle configurations. In particular, we present infinite series whose members...

Abstract Implementing complex algorithms for big data, artificial intelligence, and graph processing requires enormous effort. Succinct, declarative programs to solve problems that can be efficiently executed batching streaming data are in demand. This paper presents Nexus, a distributed Datalog evaluation system. It evaluates using the semi-naive algorithm batch incremental asynchronous iteration. Furthermore, we evaluate with aggregates determine advantages of implementing iteration on its...

A Leonardo polyhedron is a 2-manifold without boundary, embedded in Euclidean 3-space E 3 , built up of convex polygons and with the geometric symmetry (or rotation) group Platonic solid genus g ≥ 2. The polyhedra are named honour Leonardo's famous illustrations [1] (cf. also [2]). Only six combinatorially regular known: Coxeter's four skew polyhedra, polyhedral realizations maps by Klein Fricke 5. In this paper we construct infinite series equivelar (i.e. locally regular) which share some...

Abstract We discuss a polyhedral embedding of the classical Fricke-Klein regular map genus 5 in ordinary space E 3 . This polyhedron was originally discovered by Grünbaum 1999, but recently rediscovered Brehm andWills. establish isomorphism with map, and confirm its combinatorial regularity. The is among few currently known geometrically vertex-transitive polyhedra g ≥ 2, conjectured to be only this range that also combinatorially regular. contribute new polyhedron, 11, list, as 7th example....

Highly symmetric figures, such as regular polytopes, can serve a scaffolding on which spatial ( n k ) point-line configurations be built. We give several constructions using this method in dimension 3 and 4. also explore possible of obtained Cartesian products smaller ones. Using suitable powers well-chosen configurations, we obtain infinite series for both are arbitrarily large. combine the polytopal to construct further examples. Finally, formulate an incidence statement concerning (100 4...

Abstract We revisit the configuration DCD(4) of Danzer, a great inspiration for our work. This type (35 4 ) falls into an in_nite series geometric point-line configurations DCD(n). Each DCD(n) is characterized combinatorially by having Kronecker cover over Odd graph On as its Levi graph. Danzer’s deeply rooted in Pascal’s Hexagrammum Mysticum. Although combinatorial highly symmetric, we conjecture that there are no realizations with 7- or 5-fold rotational symmetry; on other hand, found...

In 2017 a first selfintersection-free polyhedral realization of Hurwitz’s regular map {3, 7}18 genus 7 was found by Michael Cuntz and the author. For any which had previously been realized as polyhedron without self-intersections in 3-space, it also possible to find such with nontrivial geometric symmetries. So is natural ask whether we can for above-mentioned corresponding version some non-trivial symmetry. The orientation-preserving combinatorial automorphism group this Hurwitz projective...

Many common data analysis tasks, such as performing hyperparameter optimization, processing a partitioned graph, and treating matrix vector of vectors, offer natural opportunities for nested-parallel operations, i.e., launching parallel operations from inside other operations. However, state-of-the-art dataflow engines, Spark Flink, do not support nested parallelism. Users must implement workarounds, causing orders magnitude slowdowns their let alone the implementation effort.

Modern data analysis tasks often involve control flow statements, such as iterations. Common examples are PageRank and K-means. To achieve scalability, developers usually implement in distributed dataflow systems, Spark Flink. However, for with these systems still either suffer from poor performance or hard to use. For example, while Flink supports iterations provides ease-of-use, is use has iterative tasks. As a result, typically have different workarounds run their jobs statements an easy...

Abstract We construct, for all d ≥ 4, a cellulation of . prove that these cellulations cannot be polytopal with maximal combinatorial symmetry. Such non-realizability phenomenon was first described in dimension 4 by Bokowski, Ewald and Kleinschmidt, and, to the knowledge author, until now there have not been any known examples higher dimensions. As starting point construction, we introduce new class (Wythoffian) uniform polytopes, which call duplexes. In proving our main result, use some...

We study relations between $(n_4)$ incidence configurations and the classical Poncelet Porism. Poncelet's result studies two conics a sequence of points lines that inscribes one conic circumscribes other. Porism states whether this closes up after $m$ steps only depends on not initial point sequence. In other words: polygons are movable. transfer motion into flexibility statement about large class configurations, which where 4 (straight) pass through each four lie line. A first instance such...

We study the geometric structure of Poncelet $n$-gons from a projective point view. In particular we present explicit constructions for certain $n$ and derive algebraic characterisations in terms bracket polynomials. Via connections polygons $(N_4)$-configurations, results this article can be used to construct large class specific movable trivial celestial 4-configurations, which up were all thought rigid require regular their construction.

When searching for small 4-configurations of points and lines, polycyclic configurations, in which every symmetry class lines contains the same number elements, have proved to be quite useful. In this paper we construct prove existence a previously unknown $(21_4)$ configuration, provides counterexample conjecture Branko Grünbaum. addition, study some its most important properties; particular, make comparison with well-known Grünbaum-Rigby configuration. We show that there are exactly two...