지원사업
학술연구/단체지원/교육 등 연구자 활동을 지속하도록 DBpia가 지원하고 있어요.
커뮤니티
연구자들이 자신의 연구와 전문성을 널리 알리고, 새로운 협력의 기회를 만들 수 있는 네트워킹 공간이에요.
이용수
초록· 키워드
오류제보하기
Go is an ancient game of great complexity and has a huge following in East Asia. It is also very rich mathematically, and can be played on any graph, although it is usually played on a square lattice. As with any game, one of the most fundamental problems is to determine the number of legal positions, or the probability that a random position is legal. A random Go position is generated using a model previously studied by the author, with each vertex being independently Black, White or Uncoloured with probabilities $q,q,1-2q$ respectively. In this paper we consider the probability of legality for two scenarios. Firstly, for an $N\times N$ square lattice graph, we show that, with $q=cN^{-\alpha}$ and $c$ and $\alpha$ constant, as $N\rightarrow\infty$ the limiting probability of legality is 0, $\exp(-2c^5)$, and 1 according as $\alpha<2/5$, $\alpha=2/5$ and $\alpha>2/5$ respectively. On the way, we investigate the behaviour of the number of captured chains (or chromons). Secondly, for a random graph on $n$ vertices with edge probability $p$ generated according to the classical Gilbert-Erd\H{o}s-R\'enyi model $\mathcal{G}(n;p)$, we classify the main situations according to their asymptotic almost sure legality or illegality. Our results draw on a variety of probabilistic and enumerative methods including linearity of expectation, second moment method, factorial moments, polyomino enumeration, giant components in random graphs, and typicality of random structures. We conclude with suggestions for further work.
목차
등록된 정보가 없습니다.
참고문헌 (24)
참고문헌 신청
N. Alon / 2003 / Partitioning into graphs with only small components / J. Combin. Theory Ser. B 87(2):231~243
N. Alon / 1992 / The Probabilistic Method / Wiley
BadukTV
E. R. Berlekamp / 1994 / Mathematical Go: Chilling Gets the Last Point / A. K. Peters
B. Bouzy / 2001 / Computer Go: an AI oriented survey / Artificial Intelligence 132(1):39~103
N. Alon / 1992 / The Probabilistic Method / Wiley
BadukTV
E. R. Berlekamp / 1994 / Mathematical Go: Chilling Gets the Last Point / A. K. Peters
B. Bouzy / 2001 / Computer Go: an AI oriented survey / Artificial Intelligence 132(1):39~103
함께 읽어보면 좋을 논문
논문 유사도에 따라 DBpia 가 추천하는 논문입니다. 함께 보면 좋을 연관 논문을 확인해보세요!
-
CHARACTERISTIC POLYNOMIALS OF SUBDIVISION GRAPHS
Advanced Studies in Contemporary Mathematics
2021 .01
-
Introduction to probabilistic computing based on random MTJs
한국자기학회 학술연구발표회 논문개요집
2020 .07
-
Graph Equations Involving Tensor Product of Graphs
Kyungpook Mathematical Journal
2017 .06
-
Induced signed graphs of some classes of graphs
Proceedings of the Jangjeon Mathematical Society
2020 .01
-
Abstract random linear operators on probabilistic unitary spaces
대한수학회지
2016 .01
-
Characteristic polynomials of oriented graphs
Proceedings of the Jangjeon Mathematical Society
2023 .04
-
Total domination number of central graphs
대한수학회보
2019 .01
-
Some Properties of q-Distance Energy
Advanced Studies in Contemporary Mathematics
2020 .01
-
New results on the F-index of graphs based on Corona-type products of graphs
Proceedings of the Jangjeon Mathematical Society
2020 .01
-
On co-well covered graphs
대한수학회논문집
2020 .01
-
Spectra of F-sum graphs and F-product graphs
Proceedings of the Jangjeon Mathematical Society
2018 .01
-
The Wiener Polynomial for the Subdivision Graph of Certain Classes of Graphs
Advanced Studies in Contemporary Mathematics
2015 .01
-
ON HARMONIOUS COLORINGS OF LEXICOGRAPHIC PRODUCT OF GRAPHS
Advanced Studies in Contemporary Mathematics
2021 .04
-
SIGNED A-POLYNOMIALS OF GRAPHS AND POINCAR´E POLYNOMIALS OF REAL TORIC MANIFOLDS
대한수학회보
2015 .01
-
On rings whose annihilating-ideal graphs are blow-ups of a class of Boolean graphs
대한수학회지
2017 .01
-
An extension of random summations of independent and identically distributed random variables
대한수학회논문집
2018 .01
-
Prediction of random effects with misspecified AFT random effect models
한국데이터정보과학회지
2022 .09
-
METRIC DIMENSION AND ITS VARIATIONS OF CHAIN GRAPHS
Proceedings of the Jangjeon Mathematical Society
2021 .07
-
ON r-DYNAMIC COLORINGS OF THE FRIENDSHIP GRAPH FAMILIES
Advanced Studies in Contemporary Mathematics
2021 .04
-
On the annihilator graph of group rings
대한수학회보
2017 .01
이 논문의 저자 정보
최근 본 자료
댓글(0)
0