Class-Uniformly Resolvable Group Divisible Structures I: Resolvable Group Divisible Designs
نویسندگان
چکیده
منابع مشابه
Class-Uniformly Resolvable Group Divisible Structures I: Resolvable Group Divisible Designs
We consider Class-Uniformly Resolvable Group Divisible Designs (CURGDD), which are resolvable group divisible designs in which each of the resolution classes has the same number of blocks of each size. We derive the fully general necessary conditions including a number of extremal bounds. We present some general constructions including a novel construction for shrinking the index of a master de...
متن کاملClass-Uniformly Resolvable Group Divisible Structures II: Frames
We consider Class-Uniformly Resolvable frames (CURFs), which are group divisible designs with partial resolution classes subject to the class-uniform condition. We derive the necessary conditions, including extremal bounds, build the foundation for general CURF constructions, including a frame variant of the λ blow-up construction from part I. We also establish a PBD-closure result. For CURFs w...
متن کاملResolvable Group Divisible Designs with Large Groups
We prove that the necessary divisibility conditions are sufficient for the existence of resolvable group divisible designs with a fixed number of sufficiently large groups. Our method combines an application of the Rees product construction with a streamlined recursion based on incomplete transversal designs. With similar techniques, we also obtain new results on decompositions of complete mult...
متن کاملResolvable group divisible designs with block size 3
A group divisible design is resolvable if there exists a partition n = {P,, Pz, . .} of p such that each part Pi is itself a partition of X. In this paper we investigate the existence of resolvable group divisible designs with K = {3}, M a singleton set, and all A. The case where M = { 1) has been solved by Ray-Chaudhuri and Wilson for I = 1, and by Hanani for all h > 1. The case where M is a s...
متن کاملResolvable Modified Group Divisible Designs with Block Size Three
A resolvable modified group divisible design (RMGDD) is an MGDD whose blocks can be partitioned into parallel classes. In this article, we investigate the existence of RMGDDs with block size three and show that the necessary conditions are also sufficient with two exceptions. # 2005 Wiley Periodicals, Inc. J Combin Designs 15: 2–14, 2007
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2004
ISSN: 1077-8926
DOI: 10.37236/1776