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Integers

A class of extensions of Restricted (s,t)-Wythoff’s game

Open Mathematics

Restricted (s, t)-Wythoff’s game, introduced by Liu et al. in 2014, is an impartial combinatorial game. We define and solve a class of games obtained from Restricted (s, t)-Wythoff’s game by adjoining to it some subsets of its P-positions as additional moves. The results show that under certain conditions they are equivalent to one case in which only one P-position is adjoined as an additional move. Furthermore, two winning strategies of exponential and polynomial are provided for the games.

A formulation of combinatorial auction via reverse convex programming.

Journal of Applied Mathematics and Decision Sciences

A morphic approach to combinatorial games : the Tribonacci case

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

We propose a variation of Wythoff’s game on three piles of tokens, in the sense that the losing positions can be derived from the Tribonacci word instead of the Fibonacci word for the two piles game. Thanks to the corresponding exotic numeration system built on the Tribonacci sequence, deciding whether a game position is losing or not can be computed in polynomial time.

A morphic approach to combinatorial games: the Tribonacci case

RAIRO - Theoretical Informatics and Applications

We propose a variation of Wythoff's game on three piles of tokens, in the sense that the losing positions can be derived from the Tribonacci word instead of the Fibonacci word for the two piles game. Thanks to the corresponding exotic numeration system built on the Tribonacci sequence, deciding whether a game position is losing or not can be computed in polynomial time.

A pairing strategy for tic-tac-toe on the integer lattice with numerous directions.

The Electronic Journal of Combinatorics [electronic only]

A solution of two-person single-suit whist.

The Electronic Journal of Combinatorics [electronic only]

An Algorithm for the Detection of Move Repetition Without the Use of Hash-Keys

The Yugoslav Journal of Operations Research

Integers

Asymptotically optimal pairing strategy for tic-tac-toe with numerous directions.

The Electronic Journal of Combinatorics [electronic only]

Aviezri Fraenkel and combinatorial games.

The Electronic Journal of Combinatorics [electronic only]

Biased positional games and small hypergraphs with large covers.

The Electronic Journal of Combinatorics [electronic only]

Blocking Wythoff Nim.

The Electronic Journal of Combinatorics [electronic only]

Coeur et nucléolus des jeux de recouvrement

RAIRO - Operations Research

A cooperative game is defined as a set of players and a cost function. The distribution of the whole cost between the players can be done using the core concept, that is the set of all undominated cost allocations which prevent players from grouping. In this paper we study a game whose cost function comes from the optimal solution of a linear integer covering problem. We give necessary and sufficient conditions for the core to be nonempty and characterize its allocations using linear programming...

Cœur et nucléolus des jeux de recouvrement

RAIRO - Operations Research - Recherche Opérationnelle

Combinatorial games: Selected bibliography with a succinct gourmet introduction.

The Electronic Journal of Combinatorics [electronic only]

Covering codes for Hats-on-a-line.

The Electronic Journal of Combinatorics [electronic only]

Integers

Discrete bidding games.

The Electronic Journal of Combinatorics [electronic only]

Dynamic one-pile blocking Nim.

The Electronic Journal of Combinatorics [electronic only]

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