相关论文: New directions in enumerative chess problems

Infinite chess is chess played on an infinite edgeless chessboard. The familiar chess pieces move about according to their usual chess rules, and each player strives to place the opposing king into checkmate. The mate-in-n problem of…

We introduce a new family of one-player games, involving the movement of coins from one configuration to another. Moves are restricted so that a coin can be placed only in a position that is adjacent to at least two other coins. The goal of…

In this thesis we enumerate standard young tableaux (SYT) of certain truncated skew shapes, which we call battery shapes. This is motivated by a chess problem. In an enumerative chess problem, the set of moves in the solution is (usually)…

We prove PSPACE-completeness of two classic types of Chess problems when generalized to n-by-n boards. A "retrograde" problem asks whether it is possible for a position to be reached from a natural starting position, i.e., whether the…

Simple stochastic games are two-player zero-sum stochastic games with turn-based moves, perfect information, and reachability winning conditions. We present two new algorithms computing the values of simple stochastic games. Both of them…

The game of best choice (also known as the secretary problem) is a model for sequential decision making with a long history and many variations. The classical setup assumes that the sequence of candidate rankings are uniformly distributed.…

We study so-called invariant games played with a fixed number $d$ of heaps of matches. A game is described by a finite list $\mathcal{M}$ of integer vectors of length $d$ specifying the legal moves. A move consists in changing the current…

Automatic chess problem or puzzle composition typically involves generating and testing various different positions, sometimes using particular piece sets. Once a position has been generated, it is then usually tested for positional…

In an investigation of the applications of Combinatorial Game Theory to chess, we construct novel mutual Zugzwang positions, explain an otherwise mysterious pawn endgame from "A Guide to Chess Endings" (Euwe and Hooper), show positions…

Bidding chess is a chess variant where instead of alternating play, players bid for the opportunity to move. Generalizing a known result on so-called Richman games, we show that for a natural class of games including bidding chess, each…

It is odd that chess grandmasters often disagree in their analysis of positions, sometimes even of simple ones, and that a grandmaster can hold his own against an powerful analytic machine such as Deep Blue. The fact that there must exist…

A classic problem in enumerative combinatorics is to count the number of derangements, that is, permutations with no fixed point. Inspired by a recent generalization to facet derangements of the hypercube by Gordon and McMahon, we…

In this paper, we address a natural question at the intersection of combinatorial game theory and computational complexity: "Can a sum of simple tepid games in canonical form be intractable?" To resolve this fundamental question, we…

We investigate the mathematics behind unshuffles, a type of card shuffle closely related to classical perfect shuffles. To perform an unshuffle, deal all the cards alternately into two piles and then stack the one pile on top of the other.…

Consider a uniformly random deck consisting of cards labelled by numbers from $1$ through $n$, possibly with repeats. A guesser guesses the top card, after which it is revealed and removed and the game continues. What is the expected number…

We study a combinatorial game derived from a problem in the German National Mathematics Competition. In this game, two players take turns removing numbers from a finite set of natural numbers, aiming to satisfy a certain divisibility…

The main challenge of combinatorial game theory is to handle combinatorial chaos, if one player knows the strategy better than his opponent, he is able to determine the exact results of a game. If both players are qualified competitor, the…

We prove computational intractability of variants of checkers: (1) deciding whether there is a move that forces the other player to win in one move is NP-complete; (2) checkers where players must always be able to jump on their turn is…

We consider a game in which a blindfolded player attempts to set $n$ counters lying on the vertices of a rotating regular $n$-gon table simultaneously to $0$. When the counters count$\pmod{m}$ we simplify the argument of Bar Yehuda, Etzion,…

Combinatorial Game Theory typically studies sequential rulesets with perfect information where two players alternate moves. There are rulesets with {\em entailing moves} that break the alternating play axiom and/or restrict the other…