منابع مشابه
Note on parameters of balanced ternary designs
Conditions under which constant block size implies constant replication number and vice versa are established for balanced ternary designs. This note is motivated by a note of almost the identical title of W. D. Wallis [2]. In a balanced binary design with constant block size, the replication number must be constant, but the converse is not true. Wallis [2] proved the following partial converse...
متن کاملNote on the parameters of balanced designs
In discussing block designs we use the usual notations and terminology of the combinatorialliterature (see, for example, [1], [2]) "balance" will always mean pairwise balance and blocks do not contain repeated elements. It is well-known that a balanced design need not have constant block-size or constant replication number. However, it is easy to show ([2, p.22J). that in any balanced design wi...
متن کاملOn construction of partially balanced n-ary designs
A new method of constructing a series of partially balanced ternary (PBT) designs is presented. In the method, we have added the corresponding rows of incidence matrices of a BIB design and a PBIB design, both obtained from single initial block with at least one element in common between them. The BIB and PBIB designs above were obtained by method of differences. We have also constructed PBT de...
متن کاملKey Predistribution Using Partially Balanced Designs in Wireless Sensor Networks
We propose two deterministic key predistribution schemes in a Wireless Sensor Network (WSN), in which sensor nodes are deployed randomly. Both the schemes are based on Partially Balanced Incomplete Block Designs (PBIBD). An important feature of our scheme is that every pair of nodes can communicate directly, making communication faster and efficient. The number of keys per node is of the order ...
متن کاملA note on balanced bipartitions
A balanced bipartition of a graph G is a bipartition V1 and V2 of V (G) such that −1 ≤ |V1| − |V2| ≤ 1. Bollobás and Scott conjectured that if G is a graph with m edges and minimum degree at least 2 then G admits a balanced bipartition V1, V2 such that max{e(V1), e(V2)} ≤ m/3, where e(Vi) denotes the number of edges of G with both ends in Vi. In this note, we prove this conjecture for graphs wi...
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ژورنال
عنوان ژورنال: The Annals of Mathematical Statistics
سال: 1954
ISSN: 0003-4851
DOI: 10.1214/aoms/1177728729