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Building blocks and tiles are an excellent way of learning about geometry and mathematics in general. There are several versions of tiles that are either snapped together or connected with magnets that can be used to introduce topics like…
We show that many well-known transforms in convex geometry (in particular, centroid body, convex floating body, and Ulam floating body) are special instances of a general construction, relying on applying sublinear expectations to random…
In this article, we study new methods for constructing uninorms on bounded lattices. First, we present new methods for constructing uninorms on bounded lattices under the additional constraints and prove that some of these constraints are…
A set of lines through the origin is called equiangular if every pair of lines defines the same angle, and the maximum size of an equiangular set of lines in $\mathbb{R}^n$ was studied extensively for the last 70 years. In this paper, we…
The first part of this note contains a review of basic properties of the variety of lines contained in an embedded projective variety and passing through a general point. In particular we provide a detailed proof that for varieties defined…
Two structures are said to be equimorphic if each embeds in the other. Such structures cannot be expected to be isomorphic, and in this paper we investigate the special case of linear orders, here also called chains. In particular we…
We produce many new complete, constant Q-curvature metrics on finitely punctured spheres by gluing together known examples. In our construction we truncate one end of each summand and glue the two summands together "end-to-end," where we've…
We study combinatorial configurations with the associated point and line graphs being strongly regular. Examples not belonging to known classes such as partial geometries and their generalizations or elliptic semiplanes are constructed.…
The concept of coreflexive set is introduced to study the structure of digraphs. New characterizations of line digraphs and nth-order line digraphs are given. Coreflexive sets also lead to another natural way of forming an intersection…
This paper discusses the question of how to recognize whether an operad is E_n (ie. equivalent to the little n-cubes operad). A construction is given which produces many new examples of E_n operads. This construction is developed in the…
In this paper, we survey and refine several results -- some previously established in the literature -- that facilitate the construction of exponential bases on planar domains with explicit control over the associated frame bounds. We apply…
We extend Bravyi and Smolin's construction for obtaining unextendible maximally entangled bases (UMEBs) from equiangular lines. We show that equiangular real projections of rank more than 1 also exhibit examples of UMEBs. These projections…
It is well established that a general pair of twisted cubic curves in complex projective space has ten common secant lines. As an initial investigation, we show that the monodromy group of the ten common secant lines over the complex…
We count the number of conics through two general points in complete intersections when this number is finite and give an application in terms of quasi-lines.
We study filling sets of simple closed curves on punctured surfaces. In particular we study lower bounds on the cardinality of sets of curves that fill and that pairwise intersect at most k times on surfaces with given genus and number of…
The projection construction has been used to construct semifields of odd characteristic using a field and a twisted semifield [Commutative semifields from projection mappings, Designs, Codes and Cryptography, 61 (2011), 187--196]. We…
We construct equivariant harmonic maps between cohomogeneity one manifolds.
We study the geometric structure of Poncelet $n$-gons from a projective point of view. In particular we present explicit constructions of Poncelet $n$-gons for certain $n$ and derive algebraic characterisations in terms of bracket…
We study equilibrium configurations of infinitely many identical particles on the real line or finitely many particles on the circle, such that the (repelling) force they exert on each other depends only on their distance. The main question…
Block designs are combinatorial structures in which each pair of a set of varieties appears together in a fixed number of blocks. Complete graphs are graphs in which every pair of vertices are adjacent. We present some new constructions of…