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Combinatorics of Go [chapter]

John Tromp, Gunnar Farnebäck
2007 Lecture Notes in Computer Science  
We present several results concerning the number of positions and games of Go.  ...  We also study the Game Tree complexity of Go, proving an upper bound on the number of possible games of (mn) L(m,n) and a lower bound of 2 2 n 2 /2 −O(n) on n × n and 2 2 n−1 on 1 × n boards, in addition  ...  idea of using Chinese Remaindering and extensive help with developing and running the file-based implementations that provided the counts for n = 14 . . . 17.  ... 
doi:10.1007/978-3-540-75538-8_8 fatcat:lpkggorpxvgjtigd3nsx4yrvqy

Guest editorial: JACO going forward

Harry Blom
2018 Journal of Algebraic Combinatorics  
in algebraic combinatorics.  ...  Ilias Kotsireas of Wilfrid Laurier University in Waterloo as the new Editor-in-Chief of the Journal of Algebraic Combinatorics (JACO). Dr.  ... 
doi:10.1007/s10801-018-0815-5 fatcat:wha2o7km65eixmvkbaposg2qmy

Mr. Paint and Mrs. Correct go Fractional

Grzegorz Gutowski
2011 Electronic Journal of Combinatorics  
We study a fractional counterpart of the on-line list colouring game "Mr. Paint and Mrs. Correct" introduced recently by Schauz.  ...  On the other hand it is known from the paper of Alon et al. that the choice ratio equals the fractional chromatic number.  ...  Paint is going to fill the lists during the game. The goal of Mrs. Correct is to incrementally construct an (L, b)-colouring ϕ from the resulting list assignment. Mr.  ... 
doi:10.37236/627 fatcat:dacb26gxjzhmzdz2og4exwzq4y

The Terwilliger Algebra of the Hypercube

Junie T Go
2002 European journal of combinatorics (Print)  
We show that T is a homomorphic image of the universal enveloping algebra of the Lie algebra sl 2 (C). We obtain an element φ of T that generates the center of T .  ...  We give an introduction to the Terwilliger algebra of a distance-regular graph, focusing on the hypercube Q D of dimension D. Let X denote the vertex set of Q D .  ...  This work was carried out when the author was an Honorary Fellow at the University of Wisconsin-Madison (January-December 1998) supported by the Department of Science and Technology, Philippines.  ... 
doi:10.1006/eujc.2000.0514 fatcat:5sbto3by5zgd5n5n7swpkk2qsm

Tight Distance-regular Graphs and the Subconstituent Algebra

Junie T. Go, Paul Terwilliger
2002 European journal of combinatorics (Print)  
Let X denote the vertex set of and f x x ∈ X. where A denotes the adjacency matrix of and E * i denotes the projection onto the ith subconstituent of with respect to x.  ...  T is called the subconstituent algebra (or Terwilliger algebra) of with respect to x.  ...  GO AND PAUL TERWILLIGER † We consider a distance-regular graph with diameter D ≥ 3, intersection numbers a i , b i , c i and eigenvalues k = θ 0 > θ 1 > · · · > θ D .  ... 
doi:10.1006/eujc.2002.0597 fatcat:ocquedjr2jdobomyhvidoln3le

Interview with Edward A. Bender

ECA, University of Haifa
2021 Enumerative Combinatorics and Applications  
Mansour: Professor Bender, first of all, we would like to thank you for accepting this interview. Would you tell us broadly what combinatorics is?  ...  Systems Analysis; A Short Course in Discrete Mathematics; Foundations of Combinatorics with Applications; Lists, Decisions and Graphs -With an Introduction to Probability.  ...  I thought I might work with one of those faculty members at Caltech. Here is what happened: • Bender: I look at it from the point of view of the benefits of going to the moon.  ... 
doi:10.54550/eca2022v2s1i1 fatcat:ozley3hc7jdwxhfhe67std6evq

Preface: The Second Malta Conference in Graph Theory and Combinatorics

Irene Sciriha, Josef Lauri, John Baptist Gauci, Peter Borg
2019 Discrete Applied Mathematics  
Further words of thanks go to all the participants who contributed to the vibrant discussions on the attractive areas of graph theory, combinatorics and their applications during the talks.  ...  This special issue of Discrete Applied Mathematics, is associated with the Second Malta Conference in Graph Theory and Combinatorics held in June 2017.  ...  theory and combinatorics.  ... 
doi:10.1016/j.dam.2019.05.016 fatcat:gwr3uufexzgbvis46sfxr4qorm

Introduction

Noga Alon, Bela Bollobas
2009 Combinatorics, probability & computing  
As this collection was going to press, we learned that the third organizer of this meeting, Professor Ingo Wegener, had passed away.  ...  We are delighted to be able to publish this collection of papers in Combinatorics, Probability and Computing, and we thank all the authors and the referees for their cooperation at all stages of the process  ... 
doi:10.1017/s0963548309009766 fatcat:5oqbe4szdnbozm3hfnnjmjsbaa

Interview with Xavier Viennot

ECA, University of Haifa
2021 Enumerative Combinatorics and Applications  
This was the starting point of nice and fruitful cooperation between our combinatorial group in LaBRI and the department of statistical mechanics at Melbourne University.  ...  We did not know at the same time, Guttmann and Enting were doing some experiments, and from the first values of the sequence, applying techniques of approximants, guess (and conjecture) the formula 124  ...  For me, I was going from the world of combinatorial algebra to the world of algebraic combinatorics.  ... 
doi:10.54550/eca2022v2s1i4 fatcat:n2kaan37zrcc3l6xf25tsg477u

Combinatoric results for graphical enumeration and the higher Catalan numbers [article]

V. U. Pierce
2007 arXiv   pre-print
We give combinatoric proofs of the formulas for the number of genus 0 and genus 1 maps.  ...  We summarize some combinatoric problems solved by the higher Catalan numbers. These problems are generalizations of the combinatoric problems solved by the Catalan numbers.  ...  A path of this type going below the x-axis will go through one of the points D k = (νk − 1, −1) . Let A ′ = (0, −ν). Lemma 2.2.  ... 
arXiv:math/0703160v1 fatcat:44jbrkrvvjaqdm4pr2freilfve

CPC volume 19 issue 4 Cover and Back matter

2010 Combinatorics, probability & computing  
This book, which fi lls a gap in the existing literature, will be of interest both to the beginner, for the clarity of exposition and the judicious choice of topics, and to the specialist, who will fi  ...  This splendid account of the modern theory of Brownian motion puts special emphasis on sample path properties and connections with harmonic functions and potential theory, without omitting such important  ...  Additive Combinatorics TERENCE TAO AND VAN H.  ... 
doi:10.1017/s0963548310000179 fatcat:zx3dfzrbnvb7fbkeefbkpbipby

CPC volume 20 issue 3 Cover and Back matter

2011 Combinatorics, probability & computing  
IP address: 207.241.231.82, on 26 Jul 2018 at 03:34:14, subject to the Cambridge Core terms of use, available at  ...  Cambridge Journals Online For further information about this journal please go to the journal website at: journals.cambridge.org/cpc https://www.cambridge.org/core/terms. https://doi.org/10.1017/S0963548311000150  ... 
doi:10.1017/s0963548311000150 fatcat:lyhqkvm7dffhvcthzi6ftiohni

CPC volume 20 issue 2 Cover and Back matter

2011 Combinatorics, probability & computing  
IP address: 207.241.231.80, on 30 Jul 2018 at 07:09:51, subject to the Cambridge Core terms of use, available at  ...  Cambridge Journals Online For further information about this journal please go to the journal website at: journals.cambridge.org/cpc https://www.cambridge.org/core/terms. https://doi.org/10.1017/S0963548311000058  ... 
doi:10.1017/s0963548311000058 fatcat:vzk6ezfk2zfjtabuxlzxyzp3di

CPC volume 21 issue 3 Cover and Back matter

2012 Combinatorics, probability & computing  
IP address: 207.241.231.83, on 28 Jul 2018 at 18:42:20, subject to the Cambridge Core terms of use, available at  ...  Cambridge Journals Online For further information about this journal please go to the journal website at: journals.cambridge.org/cpc https://www.cambridge.org/core/terms. https://doi.org/10.1017/S0963548312000132  ... 
doi:10.1017/s0963548312000132 fatcat:cyi35hlytrbztiul6o6pxw7re4

The Unity of Combinatorics

Igor Pak
2022 Notices of the American Mathematical Society  
I am grateful to Anurag Bishnoi, Alex Fink, Felix Lazebnik, Bruce Rothschild, and Richard Stanley for their helpful and interesting comments on a draft of the review.  ...  You can easily see the case for the book: curious readers want to know what's really going on....  ...  Of course areas of combinatorics beside algebraic combinatorics also have a deep relationship with other parts of mathematics. [..]  ... 
doi:10.1090/noti2397 fatcat:zkfxnbiqgfbmtdph7snyxr637m
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