Counting and Testing Dominant Polynomials

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Counting and Testing Dominant Polynomials

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On Counting Polynomials of Some Nanostructures

The Omega polynomial(x) was recently proposed by Diudea, based on the length of strips in given graph G. The Sadhana polynomial has been defined to evaluate the Sadhana index of a molecular graph. The PI polynomial is another molecular descriptor. In this paper we compute these three polynomials for some infinite classes of nanostructures.

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on counting polynomials of some nanostructures

the omega polynomial(x) was recently proposed by diudea, based on the length of stripsin given graph g. the sadhana polynomial has been defined to evaluate the sadhana index ofa molecular graph. the pi polynomial is another molecular descriptor. in this paper wecompute these three polynomials for some infinite classes of nanostructures.

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Let A ∈ F2[T ]. We say A is perfect if A coincides with the sum of all of its divisors in F2[T ]. We prove that the number of perfect polynomials A with |A| ≤ x is O (x1/12+ ) for all > 0, where |A| = 2degA. We also prove that every perfect polynomial A with 1 < |A| ≤ 1.6× 1060 is divisible by T or T + 1; that is, there are no small “odd” perfect polynomials.

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ژورنال

عنوان ژورنال: Experimental Mathematics

سال: 2015

ISSN: 1058-6458,1944-950X

DOI: 10.1080/10586458.2014.992080