منابع مشابه
On Relatively Prime Sets
Functions counting the number of subsets of {1, 2, . . . , n} having particular properties are defined by Nathanson. Here, generalizations in two directions are given. Received: 10/1/08, Revised: 3/20/09, Accepted: 3/30/09
متن کاملOn Relatively Prime Sets Counting Functions
This work is motivated by Nathanson’s recent paper on relatively prime sets and a phi function for subsets of {1, 2, 3, . . . , n}. We establish enumeration formulas for the number of relatively prime subsets and the number of relatively prime subsets of cardinality k of {1, 2, 3, . . . , n} under various constraints. Further, we show how this work links up with the study of multicompositions. ...
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Prime graph of a ring R is a graph whose vertex set is the whole set R any any two elements $x$ and $y$ of $R$ are adjacent in the graph if and only if $xRy = 0$ or $yRx = 0$. Prime graph of a ring is denoted by $PG(R)$. Directed prime graphs for non-commutative rings and connectivity in the graph are studied in the present paper. The diameter and girth of this graph are also studied in the pa...
متن کاملPartitions whose parts are pairwise relatively prime
The following problem arose in connection with our research in statistical group theory: estimate a, := the number of partitions of n into parts that are pairwise relatively prime. This differs from most problems in the theory of partitions because of the complicated relationship between the part sixes. We obtain an asymptotic formula for log a,, but leave open the challenging task of obtaining...
متن کاملWhen are Two Numerical Polynomials Relatively Prime?
Let a and b be two polynomials having numerical coeecients. We consider the question: when are a and b relatively prime? Since the coeecients of a and b are approximant, the question is the same as: when are two polynomials relatively prime, even after small perturbations of the coeecients? In this paper we provide a numeric parameter for determining that two polynomials are prime, even under s...
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ژورنال
عنوان ژورنال: International Journal of Engineering Science, Advanced Computing and Bio-Technology
سال: 2018
ISSN: 2249-5592,2249-5584
DOI: 10.26674/ijesacbt/2018/49409