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On The Hardness Of Counting And Sampling Center Strings, Christina Boucher, Mohamed Omar
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
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
Sums Of Kth Powers In The Ring Of Polynomials With Integer Coefficients, Ted Chinburg, Melvin Henriksen
All HMC Faculty Publications and Research
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.