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Let bm(n) denote the number of partitions of n into powers of m. Define σr = ε2m 2 + ε3m 3 + · · · + εrm, where εi = 0 or 1 for each i. Moreover, let cr = 1 if m is odd, and cr = 2 r−1 if m is even.… (More)

- Øystein J. Rødseth, James A. Sellers
- J. Comb. Theory, Ser. A
- 2002

The restricted binary partition function bk(n) enumerates the number of ways to represent n as n = 2a0 + 2a1 + · · ·+ 2aj with 0 ≤ a0 ≤ a1 ≤ . . . ≤ aj < k. We study the question of how large a power… (More)

- Øystein J. Rødseth, James A. Sellers, Helge Tverberg
- Eur. J. Comb.
- 2009

In 1962, S. L. Hakimi proved necessary and sufficient conditions for a given sequence of positive integers d1, d2, . . . , dn to be the degree sequence of a non–separable graph or that of a connected… (More)

- Øystein J. Rødseth
- Discrete Mathematics
- 2006

An M-partition of a positive integer m is a partition of m with as few parts as possible such that every positive integer less than m can be written as a sum of parts taken from the partition. This… (More)

- Øystein J. Rødseth
- Discrete Mathematics
- 1996

Given relatively prime integers N,a~,...,ak, a multi-connected loop network is defined as the directed graph with vertex set Z/NZ = {0, 1 . . . . . N 1}, and directed edges i ~ r :i + aj (mod N). If… (More)

- Øystein J. Rødseth, James A. Sellers, Kevin M. Courtright
- 2004

A partition n = p1+p2+· · ·+pk with 1 ≤ p1 ≤ p2 ≤ · · · ≤ pk is nonsquashing if p1+· · ·+pj ≤ pj+1 for 1 ≤ j ≤ k−1. On their way towards the solution of a certain box-stacking problem, Sloane and… (More)

Abstract. For a finite set A of positive integers, we study the partition function pA(n). This function enumerates the partitions of the positive integer n into parts in A. We give simple proofs of… (More)

- Øystein J. Rødseth
- Discrete Mathematics
- 2006

Recently, Sloane suggested the following problem: We are given n boxes, labeled 1, 2, . . . , n. For i = 1, . . . , n, box i weighs (m − 1)i grams (where m ≥ 2 is a fixed integer) and box i can… (More)

A minimal r-complete partition of an integer m is a partition of m with as few parts as possible, such that all the numbers 1, . . . , rm can be written as a sum of parts taken from the partition,… (More)

For a fixed integer m ≥ 2, we say that a partition n = p1 + p2 + · · · + pk of a natural number n is m-non-squashing if p1 ≥ 1 and (m − 1)(p1 + · · · + pj−1) ≤ pj for 2 ≤ j ≤ k. In this paper we give… (More)