Related papers: Blocking sets in chain geometries
A subset of vertices of a graph is minimal if, within all subsets of the same size, its vertex boundary is minimal. We give a complete, geometric characterization of minimal sets for the planar integer lattice X. Our characterization…
This paper is an attempt to compute the decomposition numbers of the blocks of the symmetric group which have "small defect"; that is, blocks of weight smaller than the characteristic. We present various methods for computing such…
We prove a lower and an upper bound on the number of block moves necessary to sort a permutation. We put our results in contrast with existing results on sorting by block transpositions, and raise some open questions.
Difference triangle sets are useful in many practical problems of information transmission. This correspondence studies combinatorial and computational constructions for difference triangle sets having small scopes. Our algorithms have been…
Semiconstrained systems were recently suggested as a generalization of constrained systems, commonly used in communication and data-storage applications that require certain offending subsequences be avoided. In an attempt to apply…
We propose new conjectures about the relationship between the principal blocks of finite groups for different primes and establish evidence for these conjectures.
The divergence minimization problem plays an important role in various fields. In this note, we focus on differentiable and strictly convex divergences. For some minimization problems, we show the minimizer conditions and the uniqueness of…
The method for a problem solution of expenditures reduction of computing resources and time is developed at a pattern recognition, with the way of construction of the minimum tests sets or separate minimum tests on Boolean matrixes is…
A method of constructing Markov chains on finite state spaces is provided. The chain is specified by three constraints: stationarity, dependence and marginal distributions. The generalized Pythagorean theorem in information geometry plays a…
A resolving set for a graph $G$ is a set of vertices $Q = \{q_1, ..., q_k\}$ such that, for all $p\in V(G)$ the $k$-tuple $(d(p, q_1), ..., d(p, q_k ))$ uniquely determines $p$, where $d(p, q_i)$ is considered as the minimum length of a…
The purpose of this paper is to construct topology on vague soft sets. The concept of vague soft topology is introduced and its basic properties are given.
The goal of this paper is to provide some basic structure information on derivations in finite semirings.
A way to add an extra dimension is briefly discussed.
We consider the problem of finding an orientation with minimum diameter of a connected bridgeless graph. Fomin et. al. discovered a relation between the minimum oriented diameter an the size of a minimal dominating set. We improve their…
An effective indexing scheme for clusters that enables fast structure comparison and congruence check is desperately desirable in the field of mathematics, artificial intelligence, materials science, etc. Here we introduce the concept of…
We derive a new estimate of the size of finite sets of points in metric spaces with few distances. The following applications are considered: (1) we improve the Ray-Chaudhuri--Wilson bound of the size of uniform intersecting families of…
We study the behavior of blocks in flat families of finite-dimensional algebras. In a general setting we construct a finite directed graph encoding a stratification of the base scheme according to the block structures of the fibers. This…
We prove some uniqueness results for conics of minimal area that enclose a compact, full-dimensional subset of the elliptic plane. The minimal enclosing conic is unique if its center or axes are prescribed. Moreover, we provide sufficient…
We give a geometric proof of existence of Whitney stratifications of definable sets in o-minimal structures.
We investigate minimal-perimeter configurations of two finite sets of points on the square lattice. This corresponds to a lattice version of the classical double-bubble problem. We give a detailed description of the fine geometry of…