A One-Sided Zimin Construction
نویسندگان
چکیده
A string is Abelian square-free if it contains no Abelian squares; that is, adjacent substrings which are permutations of each other. An Abelian square-free string is maximal if it cannot be extended to the left or right by concatenating alphabet symbols without introducing an Abelian square. We construct Abelian square-free finite strings which are maximal by modifying a construction of Zimin. The new construction produces maximal strings whose length as a function of alphabet size is much shorter than that in the construction described by Zimin.
منابع مشابه
Design Optimization and Construction of Double-Sided Linear Induction Motor
Linear induction motors have single and double-sided structures which are used in special applications, according to their advantages and disadvantages. Due to advantages such as lack of normal forces in double-sided type, these motors are more controllable and popular than the single-sided type, especially for transportation applications. In literature, single-sided linear induction motors ha...
متن کاملOn Searching Zimin Patterns
In the area of pattern avoidability the central role is played by special words called Zimin patterns. The symbols of these patterns are treated as variables and the rank of the pattern is its number of variables. Zimin type of a word x is introduced here as the maximum rank of a Zimin pattern matching x. We show how to compute Zimin type of a word on-line in linear time. Consequently we get a ...
متن کاملOne-Sided Interval Trees
We give an alternative treatment and extension of some results of Itoh and Mahmoud on one-sided interval trees. The proofs are based on renewal theory, including a case with mixed multiplicative and additive renewals.
متن کاملObservations On Compressed Pattern-Matching with Ranked Variables in Zimin Words
Zimin words are very special finite words which are closely related to the pattern-avoidability problem. This problem consists in testing if an instance of a given pattern with variables occurs in almost all words over any finite alphabet. The problem is not well understood, no polynomial time algorithm is known and its NP-hardness is also not known. The pattern-avoidability problem is equivale...
متن کاملThe new implicit finite difference scheme for two-sided space-time fractional partial differential equation
Fractional order partial differential equations are generalizations of classical partial differential equations. Increasingly, these models are used in applications such as fluid flow, finance and others. In this paper we examine some practical numerical methods to solve a class of initial- boundary value fractional partial differential equations with variable coefficients on a finite domain. S...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Electr. J. Comb.
دوره 8 شماره
صفحات -
تاریخ انتشار 2001