New Linear Models on RDB

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(10n-52,n) {1,3,1,4,4,11,11,...,11,3,7,6,1,1} \in M{11n-68,n) {1,3,1,5,1,4,12,12,...,12,6,2,5,6,2} \in M(12n-84,n) {1,1,2,1,1,5,13,13,...,13,4,8,2,7,7,1} \in M(13n-103,n) {1,1,1,1,5,2,14,14,...,14,6,7,2,4,7,5,1} \in M(14n-125,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.