PRIMITIVE PROPERTIES OF WORDS IN {up, uq}
CHUNHUA CAO *
School of Mathematics and Statistics, Yunnan University, 2 Cuihu North RD, Kunming, Yunnan, 650091, China
XIN LI
School of Mathematics and Statistics, Yunnan University, 2 Cuihu North RD, Kunming, Yunnan, 650091, China
DI YANG
School of Information, Yunnan University of Finance and Economics, 237 Longquan RD, Kunming, Yunnan, 650091, China
YALI YANG
School of Mathematics and Statistics, Yunnan University, 2 Cuihu North RD, Kunming, Yunnan, 650091, China
*Author to whom correspondence should be addressed.
Abstract
In 2002, Gheorghe Păun and Nicolae Son proved if u is a non-empty word and a, b are two distinct letters, then at least one of ua and ub is a primitive word. We want to discuss if the suffix words a and b in ua and ub, respectively, are not letters, then what happens. So we first prove if u is a non-empty word, p is the empty word and q is a non-empty word whose length is less than 4, then at least one of u and uq is a primitive word when uq ≠ qu. Then, we prove if u is a non-empty word and p, q are two distinct non-empty words whose lengths are less than 3, then at least one of up and uq is a primitive word when pq ≠ qp. At last, we discuss the primitive properties of words in {up, uq}, when u is a non-empty word whose length is odd or even, separately.
Keywords: Primitive word, non-primitive words