New Linear Models on RDB
Kechang Yang yangkec@163.com
Computer Science and Engineering Hunan Institute of Science & Technology PR China
Abstract
In this paper we establish several new linear models on RDB. Let a ruler have
n marks, and let its length be L. A set of models of marks distribution,
each of which makes the ruler perfect, is denoted by M(L,n). Our
main results are the following five linear models: {1,1,6,7,1,10,10,...,10,3,4,2,3}
\in M(10n52,n) {1,3,1,4,4,11,11,...,11,3,7,6,1,1} \in M{11n68,n)
{1,3,1,5,1,4,12,12,...,12,6,2,5,6,2} \in M(12n84,n) {1,1,2,1,1,5,13,13,...,13,4,8,2,7,7,1}
\in M(13n103,n) {1,1,1,1,5,2,14,14,...,14,6,7,2,4,7,5,1} \in M(14n125,n)
By the new models, in applicable range of n (<30) we have improved
the author's previous results, which were derived from the quadratic
models. Key words: complete graph, graceful label, RDB(Restricted
Difference Basis), linear model.
