Sprague-Grundy function of matroids and related hypergraphs
نویسندگان
چکیده
منابع مشابه
The Sprague-Grundy Function for Wythoff's Game
We present two new results on Wythoff’s Grundy function G. The first one is a proof that for every integer g 0, the g-values of G are within a bounded distance to their corresponding 0-values. Since the 0-values are located roughly along two diagonals, of slopes and , the g-values are contained within two strips of bounded width around those diagonals. This is a generalization of a previous res...
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We show that the Sprague-Grundy function of the game Euclid is given by g(x, y) = b|y/x− x/y|c for x, y ≥ 1.
متن کاملThe Sprague-Grundy function of the real game Euclid
The game Euclid, introduced and named by Cole and Davie, is played with a pair of nonnegative integers. The two players move alternatively, each subtracting a positive integer multiple of one of the integers from the other integer without making the result negative. The player who reduces one of the integers to zero wins. Unfortunately, the name Euclid has also been used for a subtle variation ...
متن کاملOn Calculating the Sprague-grundy Function for the Game Euclid
The two-person nim-type game Euclid, E, is played on a board. A position (a, b), or equivalently (b, a), consists of a pair of positive integers. Players alternate moves, a move consisting of decreasing the larger number in the current position by any positive multiple of the smaller number, as long as the result remains positive. The first player unable to make a move loses. Some background in...
متن کاملSprague-Grundy Values of the R-Wythoff Game
We examine the Sprague-Grundy values of the game of R-Wythoff, a restriction of Wythoff’s game introduced by Ho, where each move is either to remove a positive number of tokens from the larger pile or to remove the same number of tokens from both piles. Ho showed that the P -positions of R-Wythoff agree with those of Wythoff’s game, and found all positions of Sprague-Grundy value 1. We describe...
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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 2019
ISSN: 0304-3975
DOI: 10.1016/j.tcs.2019.09.041