相关论文: On Resolvable Golomb Rulers, Symmetric Configurati…

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.…

Normally a chess problem must have a unique solution, and is deemed unsound even if there are alternatives that differ only in the order in which the same moves are played. In an enumerative chess problem, the set of moves in the solution…

Let $n$ points be in crescent configurations in $\mathbb{R}^d$ if they lie in general position in $\mathbb{R}^d$ and determine $n-1$ distinct distances, such that for every $1 \leq i \leq n-1$ there is a distance that occurs exactly $i$…

Modern experimental methods enable the creation of self-assembly building blocks with tunable interactions, but optimally exploiting this tunability for the self-assembly of desired structures remains an important challenge. Many studies of…

We address combinatorial problems that can be formulated as minimization of a partially separable function of discrete variables (energy minimization in graphical models, weighted constraint satisfaction, pseudo-Boolean optimization, 0-1…

Conic optimization has recently emerged as a powerful tool for designing tractable and guaranteed algorithms for non-convex polynomial optimization problems. On the one hand, tractability is crucial for efficiently solving large-scale…

We focus on rational solutions or nearly-feasible rational solutions that serve as certificates of feasibility for polynomial optimization problems. We show that, under some separability conditions, certain cubic polynomially constrained…

The solvable Farb growth of a group quantifies how well-approximated the group is by its finite solvable quotients. In this note we present a new characterization of polycyclic groups which are virtually nilpotent. That is, we show that a…

We discuss group divisible designs with block size four and type $g^u b^1 (gu/2)^1$, where $u = 5$, 6 and 7. For integers $a$ and $b$, we prove the following. (i) A 4-GDD of type $(4a)^5 b^1 (10a)^1$ exists if and only if $a \ge 1$, $b…

We describe a new type of polycyclic presentations, that we will call refined solvable presentations, for polycyclic groups. These presentations are obtained by refining a series of normal subgroups with abelian sections. These…

Frame difference families, which can be obtained via a careful use of cyclotomic conditions attached to strong difference families, play an important role in direct constructions for resolvable balanced incomplete block designs. We…

We consider N-fold 4-block decomposable integer programs, which simultaneously generalize N-fold integer programs and two-stage stochastic integer programs with N scenarios. In previous work [R. Hemmecke, M. Koeppe, R. Weismantel, A…

We consider a generalization of the dining philosophers problem to arbitrary connection topologies. We focus on symmetric, fully distributed systems, and we address the problem of guaranteeing progress and lockout-freedom, even in presence…

We say that a linear space is harmonious if it is resolvable and admits an automorphism group acting sharply transitively on the points and transitively on the parallel classes. Generalizing old results by the first author et al. we present…

Studying distributed computing through the lens of algebraic topology has been the source of many significant breakthroughs during the last two decades, especially in the design of lower bounds or impossibility results for deterministic…

We study nonlinear resolvents of holomorphic generators of one-parameter semigroups acting in the open unit disk. The class of nonlinear resolvents can be studied in the framework of geometric function theory because it consists of…

Let $G$ be an almost simple group. We prove that if $x \in G$ has prime order $p \ge 5$, then there exists an involution $y$ such that $<x,y>$ is not solvable. Also, if $x$ is an involution then there exist three conjugates of $x$ that…

To make a joint decision, agents (or voters) are often required to provide their preferences as linear orders. To determine a winner, the given linear orders can be aggregated according to a voting protocol. However, in realistic settings,…

We prove a new criterion for the solvability of the finite groups, depending on the function $\psi_k(G)$ which is defined as the sum of $k$-th powers of the element orders of $G$. We show that our result can be used to show the solvability…

We prove the existence and give constructions of a $(p(k)-1)$-fold perfect resolvable $(v, k, 1)$-Mendelsohn design for any integers $v > k \ge 2$ with $v \equiv 1 \mod k$ such that there exists a finite Frobenius group whose kernel $K$ has…