Zobrazeno 1 - 10
of 599
pro vyhledávání: '"91a46"'
Autor:
Akiyama, Shigeki
We introduce a new generalization of Wythoff Nim using three piles of stones. We show that its P-positions have finite difference properties and produce a partition of positive integers. Further, we give a conjecture that the P-positions approximate
Externí odkaz:
http://arxiv.org/abs/2412.08399
It is well known that there is a duality map between the superstable configurations and the critical configurations of a graph. This was extended to all M-matrices in (Guzm\`an-Klivans 2015). We show a natural way to extend this to all $(L,M)$-chip f
Externí odkaz:
http://arxiv.org/abs/2412.02679
Autor:
Gauthier, Melanie, Huntemann, Svenja
Snort is a two-player game played on a simple graph in which the players take turns colouring vertices in their own colour, with the restriction that two adjacent vertices cannot have opposite colours. We will show that on triangular grids with one o
Externí odkaz:
http://arxiv.org/abs/2412.00849
Autor:
Shinoda, Masato
The classic game of Nim has been well-known for many years, inspiring numerous variations. One such variant is Delete Nim, where players take turns eliminating one pile of stones and splitting the remaining pile into two smaller piles. In this paper
Externí odkaz:
http://arxiv.org/abs/2411.19453
Autor:
Saunders, Ethan J., Selinger, Peter
The game of Paintbucket was recently introduced by Amundsen and Erickson. It is played on a rectangular grid of black and white pixels. The players alternately fill in one of their opponent's connected components with their own color, until the entir
Externí odkaz:
http://arxiv.org/abs/2411.19373
Mis\`ere games in general have little algebraic structure, but if the games under consideration have properties then some algebraic structure re-appears. In 2023, the class of Blocking games was identified. Mis\`ere Cricket Pitch was suggested as a p
Externí odkaz:
http://arxiv.org/abs/2411.17518
Autor:
Oginuma, Hiromi, Shinoda, Masato
The game of Nim, which has been well known for many years, has numerous variations. One such variation is Circular Nim, where piles of stones are arranged on a circumference, and players take stones from consecutive adjacent piles in one move. In thi
Externí odkaz:
http://arxiv.org/abs/2411.07497
We present a new O(k log n) algorithm of the Josephus problem. The time complexity of our algorithm is O(k log n), and this time complexity is on a par with the existing O(k log n) algorithm. We do not have any recursion overhead or stack overflow be
Externí odkaz:
http://arxiv.org/abs/2411.16696
Autor:
Davies, Alfie, Yadav, Vishal
Understanding invertibility in restricted mis\`ere play has been challenging; in particular, the possibility of non-conjugate inverses posed difficulties. Advances have been made in a few specific universes, but a general theorem was elusive. We prov
Externí odkaz:
http://arxiv.org/abs/2410.06924
Autor:
Davies, Alfie
Losing a game is difficult. Recent work of Larsson, Nowakowski, and Santos, as well as that of Siegel, has opened up enticing lines of research into partizan mis\`ere theory. The algebraic structure of mis\`ere monoids is not yet well understood. A n
Externí odkaz:
http://arxiv.org/abs/2409.17871