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- Andreas M. Hinz, Sandi Klavzar, Uros Milutinovic, Daniele Parisse, Ciril Petr
- Eur. J. Comb.
- 2005

It is known that in the Tower of Hanoi graphs there are at most two different shortest paths between any fixed pair of vertices. A formula is given that counts, for a given vertex v, the number of vertices u such that there are two shortest u, v-paths. The formula is expressed in terms of Stern’s diatomic sequence b(n) (n ≥ 0) and implies that only for… (More)

- Sandi Klavzar, Uros Milutinovic, Ciril Petr
- Discrete Applied Mathematics
- 2002

It is proved that seven different approaches to the multi-peg Tower of Hanoi problem are all equivalent. Among them the classical approaches of Stewart and Frame from 1941 can be found.

Come with us to read a new book that is coming recently. Yeah, this is a new coming book that many people really want to read will you be one of them? Of course, you should be. It will not make you feel so hard to enjoy your life. Even some people think that reading is a hard to do, you must be sure that you can do it. Hard will be felt when you have no… (More)

- Simon Aumann, Katharina A. M. Götz, Andreas M. Hinz, Ciril Petr
- Electr. J. Comb.
- 2014

In contrast to the widespread interest in the Frame-Stewart Conjecture (FSC) about the optimal number of moves in the classical Tower of Hanoi task with more than three pegs, this is the first study of the question of investigating shortest paths in Hanoi graphs H p in a more general setting. Here p stands for the number of pegs and n for the number of… (More)

- Sandi Klavzar, Uros Milutinovic, Ciril Petr
- Electronic Notes in Discrete Mathematics
- 1999

- Sandi Klavzar, Uros Milutinovic, Ciril Petr
- Ars Comb.
- 2001

Combinatorial properties of the multi-peg Tower of Hanoi problem on n discs and p pegs are studied. Top-maps are introduced as maps which reflect topmost discs of regular states. We study these maps from several points of view. We also count the number of edges in graphs of the multi-peg Tower of Hanoi problem and in this way obtain some combinatorial… (More)

- Andreas M. Hinz, Ciril Petr
- Electronic Notes in Discrete Mathematics
- 2016

- STERN POLYNOMIALS, Sandi Klavžar, Uroš Milutinović, Ciril Petr
- 2005

Stern polynomials Bk(t), k ≥ 0, t ∈ R, are introduced in the following way: B0(t) = 0, B1(t) = 1, B2n(t) = tBn(t), and B2n+1(t) = Bn+1(t) + Bn(t). It is shown that Bn(t) has a simple explicit representation in terms of the hyperbinary representations of n − 1 and that B 2n−1(0) equals the number of 1’s in the standard Gray code for n−1. It is also proved… (More)

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