Kazumori Masamoto i, Norihiko Misawa2, Takakazu Kaneko 3, Reiko Kikuno4 and Hiroyuki Toh 4 i BiologicalLaberatot:y. Fkecutty ofEducation, Kumameto Uhiversity. Kumamote, 860 Jopan 2 CentratLaboratoriesforKby Tleehnoiogy. Kirin Brewenyy Co., Ltd., i-f3-5 flikuura. Kanazawa-ku, Ybkohama, Kanagawa, 236 Japan3 Kazusa DNA Research Institute, J532-3 Yana, Kisarazu, Chiba, 292 Jopan 4 Biomolecular Engi...

The λ-number of a graph G is the minimum value λ such that G admits a labeling with labels from {0, 1, . . . , λ} where vertices at distance two get different labels and adjacent vertices get labels that are at least two apart. Sierpiński graphs S(n, k) generalize the Tower of Hanoi graphs—the graph S(n, 3) is isomorphic to the graph of the Tower of Hanoi with n disks. It is proved that for any...

Finite dimensional representations of the Hanoi Towers group are used to calculate the spectra of the finite graphs associated to the Hanoi Towers Game on three pegs (the group serves as a renorm group for the game). These graphs are Schreier graphs of the action of the Hanoi Towers group on the levels of the rooted ternary tree. The spectrum of the limiting graph (Schreir graph of the action o...

The generalized Tower of Hanoi problem with h ≥ 4 pegs is known to require a sub-exponentially fast growing number of moves in order to transfer a pile of n disks from one peg to another. In this paper we study the Pathh variant, where the pegs are placed along a line, and disks can be moved from a peg to its nearest neighbor(s) only. Whereas in the simple variant there are h(h−1)/2 possible bi...

This paper develops an account of the meaning and use of various types of legal claims, and uses this account to inform debates about the nature and normativity of law. The account draws on a more general framework for implementing a contextualist semantics and pragmatics, called Discourse Contextualism (Silk 2014b). The aim of Discourse Contextualism is to derive the apparent normativity of cl...

In this paper we propose a theoretical framework of distributed representations and a methodology of representational analysis for the study of distributed cognitive tasksÑtasks that require the processing of information distributed across the internal mind and the external environment. The basic principle of distributed representations is that the representational system of a distributed cogni...

The objective of this study was to redesign the Tower of Hanoi (TOH) in order to increase the reliability and explore the validity of the task. In order to achieve this goal, a two-phase process was undertaken. In Phase 1, the TOH item pool was enlarged from 12 items to 60 items, and the task was administered to a sample of college students (N = 81). The 22 most homogeneous items for the final ...

The cyclic Tower of Hanoi puzzle is similar to the traditional tower puzzle, but with the added restriction that all disks move between pegs in a clockwise direction, from peg A to B, from B to C, or from C to A. Many aspects of this puzzle have been analyzed, including the average distance in the state digraph from a random state to a designated goal state in which all disks are on one peg. Us...

We consider the problem of unfolding lattice polygons embedded on the surface of some classes of lattice polyhedra. We show that an unknotted lattice polygon embedded on a lattice orthotube or orthotree can be convexified in O(n) moves and time, and a lattice polygon embedded on a lattice Tower of Hanoi or Manhattan Tower can be convexified in O(n) moves and time.

Once upon a time, there were two puzzles. One was the Towers of Hanoi invented or introduced by Eduardo Lucas in 1883. The other was Spin-Out patented by William Keister in 1972. There are many stories about these puzzles. Some of these stories hint or claim that these puzzles have an intimate relationship with the Gray codes invented by Frank Gray in 1947. Here, we wish to show how these puzzl...