Topic
Wythoff array
About: Wythoff array is a research topic. Over the lifetime, 36 publications have been published within this topic receiving 435 citations.
Papers
TL;DR: In the Wythoff game, a player may remove any positive number of tokens from a single pile, or he may take from both piles, provided that I k 11 0, is an N-position for every a; the Next player moves to (0, 0) and wins as discussed by the authors.
Abstract: 1. Wythoff Games. Let a be a positive integer. Given two piles of tokens, two players move alternately. The moves are of two types: a player may remove any positive number of tokens from a single pile, or he may take from both piles, say k (> 0) from one and 1 (> 0) from the other, provided that I k 11 0, is an N-position for every a; the Next player moves to (0, 0) and wins. For a = 2, the position (1, 3) is a P-position: if Next moves to (0, 3), (0,2) or (0, 1), then Previous, using a move of the first type, moves to (0, 0) and wins. If Next moves to (1, 2) or to (1, 1), then Previous, using a move of the second type, can again move to (0, 0). The set of all P-positions is denoted by P, and the set of all N-positions by N.
122 citations
TL;DR: Recursive, algebraic and arithmetic strategies for winning generalized Wythoff games in misere play are given and the notion of cedar trees, a subset of binary trees, is introduced and used for consolidating these and the normal play strategies.
41 citations
TL;DR: The sets of the losing positions of geometrical extensions of Wythoff's game, where allowed moves are considered according to a set of vectors, are given, and a polynomial way to decide whether a game position is losing or not is given.
39 citations
TL;DR: A rewarding method for generating a new game with three subsets of its P-positions as moves, resulting in three different classes of games.
37 citations
Journal Article•
TL;DR: This work considers what happens when the rules for removing from both heaps are modified in various ways, including Nim and Wythoff's games.
Abstract: The P positions of both two-heap Nim and Wythoff's games are easy to describe, more so in the former than in the latter. Calculating the actual G values is easy for Nim but seemingly hard for Wythoff's game. We consider what happens when the rules for removing from both heaps are modified in various ways.
31 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2017 | 1 |
| 2016 | 1 |
| 2015 | 4 |
| 2014 | 3 |
| 2013 | 3 |
| 2012 | 2 |