10 citations · 18 across the 12 of their papers we have counts for
13 papers · 1 filter
Cyclic impartial games with carry-on moves
Tomoaki Abuku, Alda Carvalho, Urban Larsson +3
In an impartial combinatorial game, both players have the same options in the game and all its subpositions. The classical Sprague-Grundy Theory was developed for short impartial g…
Affine Normal Play
Urban Larsson, Richard J. Nowakowski, Carlos P. Santos
There are many combinatorial games in which a move can terminate the game, such as a checkmate in chess. These moves give rise to diverse situations that fall outside the scope of…
A complete solution for the partisan chocolate game
Tomoaki Abuku, Hikaru Manabe, Richard J. Nowakowski +2
The class of Poset Take-Away games includes many interesting and difficult games. Playing on an -dimensional positive quadrant (the origin being the bottom of the poset) gives r…
Indecomposable combinatorial games
Michael Fisher, Neil A. McKay, Rebecca Milley +2
In Combinatorial Game Theory, short game forms are defined recursively over all the positions the two players are allowed to move to. A form is decomposable if it can be expressed…
Infinitely many absolute universes
U. Larsson, R. J. Nowakowski, C. P. Santos
Absolute combinatorial game theory was recently developed as a unifying tool for constructive/local game comparison (Larsson et al. 2018). The theory concerns {\em parental univers…
Impartial games with entailing moves
Urban Larsson, Richard J. Nowakowski, Carlos P. Santos
Combinatorial Game Theory has also been called `additive game theory', whenever the analysis involves sums of independent game components. Such {\em disjunctive sums} invoke compar…
Ordinal Sums, Clockwise Hackenbush, and Domino Shave
Alda Carvalho, Melissa A. Huggan, Richard J. Nowakowski +1
We present two rulesets, Domino Shave and Clockwise Hackenbush. The first is somehow natural and, as special cases, includes Stirling Shave and Hetyei's Bernoulli game. Clockwise H…
Invertible Elements of the Misere Dicotic Universe
Michael Fisher, Richard Nowakowski, Carlos Pereira Dos Santos
We present a characterization of the invertible elements of the misere dicotic universe.
Progress on misère dead ends: game comparison, canonical form, and conjugate inverses
Urban Larsson, Rebecca Milley, Richard Nowakowski +2
This paper addresses several significant gaps in the theory of restricted misère play (Plambeck, Siegel 2008), primarily in the well-studied universe of dead-ending games, $\mathca…
When game comparison becomes play: Absolutely Categorical Game Theory
Urban Larsson, Richard J. Nowakowski, Carlos P. Santos
Absolute Universes of combinatorial games, as defined in a recent paper by the same authors, include many standard short normal- misère- and scoring-play monoids. In this note we s…
Absolute Combinatorial Game Theory
Urban Larsson, Richard J. Nowakowski, Carlos P. Santos
We propose a unifying additive theory for standard conventions in Combinatorial Game Theory, including normal-, misère- and scoring-play, studied by Berlekamp, Conway, Dorbec, Etti…
Guaranteed Scoring Games
Urban Larsson, João P. Neto, Richard J. Nowakowski +1
The class of Guaranteed Scoring Games (GS) are two-player combinatorial games with the property that Normal-play games (Conway et. al.) are ordered embedded into GS. They include,…
When waiting moves you in scoring combinatorial games
Urban Larsson, Richard J. Nowakowski, Carlos P. Santos
Combinatorial Scoring games, with the property `extra pass moves for a player does no harm', are characterized. The characterization involves an order embedding of Conway's Normal-…