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- William Y. C. Chen, David G. L. Wang, Iris F. Zhang
- Eur. J. Comb.
- 2009

We introduce the notion of arithmetic progression blocks or mAP blocks of Z n , which can be represented as sequences of the form (x, x + m, x + 2m,. .. , x + (i − 1)m) (mod n). Then we consider the problem of partitioning Z n into mAP blocks. We show that subject to a technical condition, the number of partitions of Z n into mAP blocks of a given type is… (More)

- William Y. C. Chen, Amy M. Fu, Iris F. Zhang
- Discrete Mathematics
- 2009

We observe that the classical Faulhaber's theorem on sums of odd powers also holds for an arbitrary arithmetic progression, namely, the odd power sums of any arithmetic progression a+ b, a+ 2b,. .. , a+ nb is a polynomial in na+ n(n + 1)b/2. While this assertion can be deduced from the original Fauhalber's theorem, we give an alternative formula in terms of… (More)

- Amy M. Fu, Iris F. Zhang
- Graphs and Combinatorics
- 2010

We show that the classical Faulhaber's theorem on sums of odd powers also holds for an arbitrary arithmetic progression, namely, the odd power sums of any arithmetic progression a + b, a + 2b,. .. , a + nb is a polynomial in na + n(n + 1)b/2. The coefficients of these polynomials are given in terms of the Bernoulli polynomials. Following Knuth's approach by… (More)

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