Related papers: Construction of 3-Designs Using (1,\sigma)-Resolut…
Simplicial arrangements are classical objects in discrete geometry. Their classification remains an open problem but there is a list conjectured to be complete at least for rank three. A further important class in the theory of hyperplane…
Our main result is the construction of symmetric Hadamard matrices of order q(1 + q) where q is a prime power congruent to 3 mod 8.
In this paper, we present an approach to automated solving of triangle ruler-and-compass construction problems using finite-domain constraint solvers. The constraint model is described in the MiniZinc modeling language, and is based on the…
Resolution and subtyping are two common mechanisms in programming languages. Resolution is used by features such as type classes or Scala-style implicits to synthesize values automatically from contextual type information. Subtyping is…
We formalize an existing computability-theoretic method of presenting first-order structures whose domains have the cardinality of the continuum. Work using these methods until now has emphasized their topological properties. We shift the…
This paper considers some different measures for how additively structured a convex set can be. The main result gives a construction of a convex set $A$ containing $\Omega(|A|^{3/2})$ three-term arithmetic progressions.
Geodesic rays of class C^{1,1} are constructed for any test configuration of a positive line bundle L on X using resolution of singularities. The construction reduces to finding a subsolution of the corresponding Monge-Ampere equation.…
Resolvable designs with two blocks per replicate are studied from an optimality perspective. Because in practice the number of replicates is typically less than the number of treatments, arguments can be based on the dual of the information…
The approach to the constructing explicit solutions of the recurrence relations for multi-loop integrals are suggested. The resulting formulas demonstrate a high efficiency, at least for 3-loop vacuum integrals case. They also produce a new…
Combinatorial $t$-designs have nice applications in coding theory, finite geometries and several engineering areas. There are two major methods of constructing $t$-designs. One of them is via group actions of certain permutation groups…
We provide partial implementations of von Neumann's universal constructor and universal copier, starting out with three types of simple building blocks using minimal assumptions. Using the same principles, we also construct Turing machines.…
We study the interaction of structural subtyping with parametric polymorphism and recursively defined type constructors. Although structural subtyping is undecidable in this setting, we describe a notion of parametricity for type…
We construct the minimal resolutions of three classes of monomial ideals: dominant, 1-semidominant, and 2-semidominant ideals. The families of dominant and 1-semidominant ideals extend those of complete and almost complete intersections. We…
Many natural decision problems can be formulated as constraint satisfaction problems for reducts $\mathbb{A}$ of finitely bounded homogeneous structures. This class of problems is a large generalisation of the class of CSPs over finite…
Reference resolution on extended texts (several thousand references) cannot be evaluated manually. An evaluation algorithm has been proposed for the MUC tests, using equivalence classes for the coreference relation. However, we show here…
We give an exact criterion of a conjecture of L.M.Kelly to hold true which is stated as follows. If there is a finite family $\Sigma$ of mutually skew lines in $\mathbb{R}^l,l\geq 4$ such that the three dimensional affine span (hull) of…
A fundamental fact for the algebraic theory of constraint satisfaction problems (CSPs) over a fixed template is that pp-interpretations between at most countable \omega-categorical relational structures have two algebraic counterparts for…
The design space for a self-assembled multicomponent objects ranges from a solution in which every building block is unique to one with the minimum number of distinct building blocks that unambiguously define the target structure. Using a…
Determinants of structured matrices play a fundamental role in both pure and applied mathematics, with wide-ranging applications in linear algebra, combinatorics, coding theory, and numerical analysis. In this work, the enumeration of…
In this paper the 3-way intersection problem for $S(2,4,v)$ designs is investigated. Let $b_{v}=\frac {v(v-1)}{12}$ and $I_{3}[v]=\{0,1,...,b_{v}\}\setminus\{b_{v}-7,b_{v}-6,b_{v}-5,b_{v}-4,b_{v}-3,b_{v}-2,b_{v}-1\}$. Let $J_{3}[v]=\{k|$…