Related papers: Strong Convergence in Posets
Partially-ordered set games, also called poset games, are a class of two-player combinatorial games. The playing field consists of a set of elements, some of which are greater than other elements. Two players take turns removing an element…
A poset game is a two-player game played over a partially ordered set (poset) in which the players alternate choosing an element of the poset, removing it and all elements greater than it. The first player unable to select an element of the…
We propose a generalization of positional games, supplementing them with a restriction on the order in which the elements of the board are allowed to be claimed. We introduce poset positional games, which are positional games with an…
In sorting situations where the final destination of each item is known, it is natural to repeatedly choose items and place them where they belong, allowing the intervening items to shift by one to make room. (In fact, a special case of…
We investigate how robust the results of committee elections are to small changes in the input preference orders, depending on the voting rules used. We find that for typical rules the effect of making a single swap of adjacent candidates…
Positional games are a well-studied class of combinatorial game. In their usual form, two players take turns to play moves in a set (`the board'), and certain subsets are designated as `winning': the first person to occupy such a set wins…
Duch\^ene and Rigo introduced the notion of invariance for take-away games on heaps. Roughly speaking, these are games whose rulesets do not depend on the position. Given a sequence $S$ of positive tuples of integers, the question of…
This paper studies sequential quantum games under the assumption that the moves of the players are drawn from groups and not just plain sets. The extra group structure makes possible to easily derive some very general results characterizing…
A poset has the non-messing-up property if it has two covering sets of disjoint saturated chains so that for any labeling of the poset, sorting the labels along one set of chains and then sorting the labels along the other set yields a…
We classify finite posets with a particular sorting property, generalizing a result for rectangular arrays. Each poset is covered by two sets of disjoint saturated chains such that, for any original labeling, after sorting the labels along…
A notion of combinatorial game over a partially ordered set of atomic outcomes was recently introduced by Selinger. These games are appropriate for describing the value of positions in Hex and other monotone set coloring games. It is…
In this paper, we consider a game beginning with a multiset of elements from a group. On a move, two elements are replaced by their sum. This is a no strategy game, and can be modeled as a graded poset with the rank of a node equal to the…
Strong placement games (SP-games) are a class of combinatorial games whose structure allows one to describe the game via simplicial complexes. A natural question is whether well-known invariants of combinatorial games, such as "game value",…
We study two new parameters for finite posets motivated by the problem of efficiently determining the set of successors of a given element. A plane map of a poset $P=(X,\leq)$ is an injective mapping of $X$ into the Cartesian plane…
A finite impartial game is a two-player game in which the players take turns making moves and the game ends after finitely many moves. In this paper, we study a class of finite impartial games introduced by H.~Lenstra, which we call coin…
In set theory without the axiom of regularity, we consider a game in which two players choose in turn an element of a given set, an element of this element, etc.; a player wins if its adversary cannot make any next move. Sets that are…
We study the space requirements of a sorting algorithm where only items that at the end will be adjacent are kept together. This is equivalent to the following combinatorial problem: Consider a string of fixed length n that starts as a…
We consider a setting in which a principal gets to choose which game from some given set is played by a group of agents. The principal would like to choose a game that favors one of the players, the social preferences of the players, or the…
We begin by reviewing and proving the basic facts of combinatorial game theory. We then consider scoring games (also known as Milnor games or positional games), focusing on the "fixed-length" games for which all sequences of play terminate…
Poset games are a class of combinatorial game that remain unsolved. Soltys and Wilson proved that computing wining strategies is in \textbf{PSPACE} and aside from special cases such as Nim and N-Free games, \textbf{P} time algorithms for…