Concerning 'Some Plain Words'

Complexity of Problems Concerning Reset Words for Some Partial Cases of Automata

A word w is called a reset word for a deterministic finite automaton A if it maps all states of A to one state. A word w is called a compressing to M states for a deterministic finite automaton A if it maps all states of A to at most M states. We consider several subclasses of automata: aperiodic, Dtrivial, monotonic, partially monotonic automata and automata with a zero state. For these subcla...

Counter-intuitive answers to some questions concerning minimal-palindromic extensions of binary words

In [Š. Holub & K. Saari, On highly palindromic words, Discrete Appl. Math. 157 (2009), 953–959] the authors proposed to measure the degree of “palindromicity” of a binary word w by ratio |rws| |w| , where the word rws is minimal-palindromic—that is, does not contain palindromic subwords of length greater than ⌈ |w| 2 ⌉ —and the length |r|+|s| is as small as possible. It was asked whether the wo...

Some Results concerning Pythagorean Triplets

By using a computer program devised by M. Creutz, we were able to determine all Pythagoeran triplets for which z ^ 300. At this point, a distinction must must be made between P-triplets for which x9 y9 and z have no common divisor [the so-called "primitive solutions" of (1)] and P-triplets which are related to the primitive solutions by multiplication by a common integer factor k. So, if Xi9y^9...

Some inequalities concerning Smarandache's function

The objectives of this article are to study the sum IS(d) and to find some upper din bounds for Smarandache's function. This sum is proved to satisfy the inequality IS(d) ~ n at most all the composite numbers, Using this inequality, some new din upper bounds for Smarandache's function are found. These bounds improve the well-known inequality Sen) ~ n.

Burns — Some Concepts Concerning Treatment