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On Ternary Inclusion-Exclusion Polynomials
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Gennady Bachman
Published/Copyright:
November 5, 2010
Abstract
Taking a combinatorial point of view on cyclotomic polynomials leads to a larger class of polynomials we shall call the inclusion-exclusion polynomials. This gives a more appropriate setting for certain types of questions about the coefficients of these polynomials. After establishing some basic properties of inclusion-exclusion polynomials we turn to a detailed study of the structure of ternary inclusion-exclusion polynomials. The latter subclass is exemplified by cyclotomic polynomials Φpqr, where p < q < r are odd primes. Our main result is that the set of coefficients of Φpqr is simply a string of consecutive integers which depends only on the residue class of r modulo pq.
Received: 2009-12-12
Accepted: 2010-06-05
Published Online: 2010-11-05
Published in Print: 2010-November
© de Gruyter 2010
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Articles in the same Issue
- Some Divisibility Properties of Binomial Coefficients and the Converse of Wolstenholme's Theorem
- On the Iteration of a Function Related to Euler's φ-Function
- An Explicit Evaluation of the Gosper Sum
- On the Frobenius Problem for {ak, ak + 1, ak + a, . . . , ak + ak−1}
- Generalizing the Combinatorics of Binomial Coefficients via -Nomials
- Finding Almost Squares V
- On Relatively Prime Subsets and Supersets
- Reformed Permutations in Mousetrap and Its Generalizations
- On Ternary Inclusion-Exclusion Polynomials
- Sums and Products of Distinct Sets and Distinct Elements in ℂ
