Games-at-Dal 2023
August 2-4, Dalhousie University
August 2-4, Dalhousie University
Games-at-Dal 2023 will take place at Dalhousie University in Halifax, Nova Scotia on August 2-4. The meeting follows the format of previous Games-at-Dal meetings. It is designed to bring together researchers in CGT. Since space is limited (max. 20), attendance is by invitation only. Please contact one of us if you are interested in attending and/or have suggestions for research problems. There is no cost for attending.
Schedule
Wednesday, Aug 2
9:00-9:30: Meet & Greet
9:30-12:30: Talks (abstracts below)
9:30-9:55 Helena Verrill
10:00-10:25 Isaac Meetsma
10:30-11:00 Coffee break
11:00-11:25 Alda Carvalho
11:30-11:55 Tom Maciosowski
12:00-12:25 Carlos Santos
12:30-2:00: Lunch
2:00-4:00: Preliminary discussions of open problems (suggestions below)
Thursday, Aug 3 & Friday, Aug 4
9:30-12:00: Morning problem session
12:00-1:30: Lunch
1:30-4:00: Afternoon problem session
Organizers:
Svenja Huntemann (svenja.huntemann@msvu.ca)
Richard Nowakowski (r.nowakowski@dal.ca)
Expected attendees:
Alda Carvalho (DCeT, Universidade Aberta & CEMAPRE/REM, University of Lisbon, Portugal)
Alfie Davis (Memorial University)
Aaron Dwyer (Carleton University)
Svenja Huntemann (Mount Saint Vincent University)
Tom Maciosowski (Concordia University of Edmonton)
Isaac Meetsma (Concordia University of Edmonton)
Rebecca Milley (Memorial University)
Richard Nowakowski (Dalhousie University)
Carlos Santos (Center for Mathematics and Applications (NovaMath), FCT NOVA)
Helena Verrill (Warwick University)
Abstracts
Alda Carvalho: «All is number»? Not so easy, Mr. Pythagoras
We present a method to evaluate if a ruleset only has positions whose game values are numbers.
(Joint work with Melissa Huggan, Richard J. Nowakowski, and Carlos Pereira dos Santos)
Tom Maciosowski: High Temperature Positions in Domineering
Domineering is a partizan game where two players have a collection of dominoes which they place on the grid in turn, covering up squares. One player places tiles vertically, while the other places them horizontally, the first player who cannot move loses. We have developed a program that enables a parallel exhaustive search of Domineering positions with high temperatures.
Isaac Meetsma: Nim Values of Distance Games
Distance games are a generalization of Node Kayles where on each move, the played upon vertices and any vertices that are a distance within a given distance set are considered unplayable. We look at impartial distance games played on a variety of graph families, testing for periodicity.
Carlos Santos: Surveying Combinatorial Game Theory monoids: exploring the algebraic structure of different restrictions
The classic order relation employed in Combinatorial Game Theory asserts that G>=H when Left can exchange H for G in all contexts without incurring any disadvantage. "Contexts" refer to "disjunctive sums", meaning that Left can accept exchanging H+X for G+X, regardless of the game form X. In the early developments of CGT, X encompassed all possible game forms. Recently, much research has been conducted by restricting the range of X to a subclass of forms F (modulo F). In the case of the misère-play convention, it is possible to obtain monoids with "more structure" than the monoid without any restrictions. Also, in Scoring CGT, interesting monoids can be obtained. Furthermore, Absolute Combinatorial Game Theory has been recently developed as a unifying tool for constructive/local game comparison, giving some general results applicable to any parental restriction. The purpose of this talk is to offer a concise overview of the current advancements in studying these types of structures. The talk will not include any proofs but will focus on delivering an organized exposition that facilitates a general and intuitive understanding of the topic for the audience.
Helena Verrill: The Grundy values of the cut game C(1,2)
This is joint work with Alfie Davies on a formula for the Grundy values of the cut game C(1,2). This is a heap game where play consists of splitting a heap into 1 or 2 piles. The behaviour of the Grundy numbers for the C(1,2) game appears to be somewhat different from the other cut games considered by Dailly, Duchene, Larsson, Paris, who's paper inspired this work.
Suggested Problems for Research Sessions
1) (suggested by Mckay, Milley, RJN, Santos) Misere CRICKET PITCH: example of a new universe of misere games (where if G and H are in the universe then for any misere game X, if G+X \geq H+X then G \geq H). From the normal play version, there is a hint of an ordinal sum description for CRICKET PITCH (Angela Siegel’s PhD Thesis). Any option-closed game is in the class, but MAZE is probably too difficult. Not sure about MAIZE (only one step at at time).
2) (suggested by Santos) Subtraction games with a single addition, e.g., S= (1,2,3,-1) means can subtract 1, 2, or 3 or add 1. This is loopy. The Fraenkel infinite nimber algorithm is important.
3) (suggested by Nowakowski) Quicksort as a game (see https://www.diva-portal.org/smash/get/diva2:935354/FULLTEXT01.pdf) The partizan version has Left pivoting on even integers, Right on odd, this is all-small (or dicotic if we want to look at the misere version). The impartial version (two games: pivot on a integer, or half-integer) has not been solved.