Volume 6, 2000, Number 3

Volume 6Number 1Number 2 ▷ Number 3 ▷ Number 4

Convolutions for Fermat polynomials and generalized Fibonacci and Lucas polynomials
Original research paper. Pages 69–81
A. Horadam
Full paper (PDF, 414 Kb)

Regular class division of integers mod r
Original research paper. Pages 82–87
P. Haukkanen
Full paper (PDF, 183 Kb)

Enumeration of integer k-gons with perimeter n
Original research paper. Pages 88–99
K. Atanassov, S. Dantchev and A. Shannon
Full paper (PDF, 593 Kb) | Abstract

We consider the following enumeration problem: how many are there ’’distinct” k-gons with integer sides and perimeter n. A solution is known for k = 3 when ’’distinct” means ”non-congruent” . This does not hold in the general case since for k > 3 a k-gon is not uniquely determined by its side lengths. We define the concept ’’distinct” in an appropriate way and reduce the problem to an enumeration of all distinct integer labels on the sides of a fixed regular k-gone satisfying a given condition. This enumeration can be done by the well known Polya’s Theory of Counting. The simple structure of the considered objects (a regular k-gon and the dihedral group of order k) allows us to prove our results in an alternative way using only elementary concepts and techniques from Group Theory and Number Theory

An elementary identity
Original research paper. Page 100
K. Atanassov
Full paper (PDF, 43 Kb)

Volume 6Number 1Number 2 ▷ Number 3 ▷ Number 4

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