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On The Hardness Of Counting And Sampling Center Strings, Christina Boucher, Mohamed Omar Jan 2012

On The Hardness Of Counting And Sampling Center Strings, Christina Boucher, Mohamed Omar

All HMC Faculty Publications and Research

Given a set S of n strings, each of length ℓ, and a nonnegative value d, we define a center string as a string of length ` that has Hamming distance at most d from each string in S. The #CLOSEST STRING problem aims to determine the number of center strings for a given set of strings S and input parameters n, ℓ, and d. We show #CLOSEST STRING is impossible to solve exactly or even approximately in polynomial time, and that restricting #CLOSEST STRING so that any one of the parameters n, ℓ, or d is fixed leads to …


The Probability Of Relatively Prime Polynomials, Arthur T. Benjamin, Curtis D. Bennet Jun 2007

The Probability Of Relatively Prime Polynomials, Arthur T. Benjamin, Curtis D. Bennet

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No abstract provided in this article.


Sums Of Kth Powers In The Ring Of Polynomials With Integer Coefficients, Ted Chinburg, Melvin Henriksen Jan 1975

Sums Of Kth Powers In The Ring Of Polynomials With Integer Coefficients, Ted Chinburg, Melvin Henriksen

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A working through of two theorems.

Suppose R is a ring with identity element and k is a positive integer. Let J(k, R) denote the subring of R generated by its kth powers. If Z denotes the ring of integers, then G(k, R) = {a ∈ Z: aR ⊂ J(k, R)} is an ideal of Z.