Related papers: The Trees of Hanoi
Simple games cover voting systems in which a single alternative, such as a bill or an amendment, is pitted against the status quo. A simple game or a yes-no voting system is a set of rules that specifies exactly which collections of ``yea''…
The famous Tower of Hanoi puzzle involves moving $n$ discs of distinct sizes from one of $p\geq 3$ pegs (traditionally $p=3$) to another of the pegs, subject to the constraints that only one disc may be moved at a time, and no disc can ever…
Attack--defense trees are used to describe security weaknesses of a system and possible countermeasures. In this paper, the connection between attack--defense trees and game theory is made explicit. We show that attack--defense trees and…
From the standpoint of game theory, dominoes is a game that has not received much attention (specially the variety known as draw). It is usually thought that this game is already solved, given general results in game theory. However, the…
We study a generalized binary search problem on the line and general trees. On the line (e.g., a sorted array), binary search finds a target node in $O(\log n)$ queries in the worst case, where $n$ is the number of nodes. In situations with…
Consider the restricted Hanoi graphs which correspond to the variants of the famous Tower of Hanoi problem with multiple pegs where moves of the discs are restricted throughout the arcs of a movement digraph whose vertices represent the…
The number of spanning trees of a graph is an important invariant related to topological and dynamic properties of the graph, such as its reliability, communication aspects, synchronization, and so on. However, the practical enumeration of…
We will describe a combinatorial game that models the problem of resolution of singularities of algebraic varieties over a field of characteristic zero. By giving a winning strategy for this game, we give another proof of the existence of…
We consider two-player random extensive form games where the payoffs at the leaves are independently drawn uniformly at random from a given feasible set C. We study the asymptotic distribution of the subgame perfect equilibrium outcome for…
We apply several quantization schemes to simple versions of the Chinos game. Classically, for two players with one coin each, there is a symmetric stable strategy that allows each player to win half of the times on average. A partial…
More than a century after its proposal, the Towers of Hanoi puzzle with 4 pegs was solved by Thierry Bousch in a breakthrough paper in 2014. The general problem with p pegs is still open, with the best lower bound on the minimum number of…
Our theme bases on the classical Hanoi Towers Problem. In this paper we will define a new problem, permitting some positions, that were not legal in the classical problem. Our goal is to find an optimal (shortest possible) sequence of…
One of the main virtues of trees is to represent formal solutions of various functional equations which can be cast in the form of fixed point problems. Basic examples include differential equations and functional (Lagrange) inversion in…
Recently, Han discovered two formulas involving binary trees which have the interestig property that hooklengths appear as exponents. The purpose of this note is to give a probabilistic proof of one of Han's formulas. Yang has generalized…
Holonomic equations are recursive equations which allow computing efficiently numbers of combinatoric objects. R{\'e}my showed that the holonomic equation associated with binary trees yields an efficient linear random generator of binary…
Aim: Present a systematic development of part of the theory of combinatorial games from the ground up. Approach: Computational complexity. Combinatorial games are completely determined; the questions of interest are efficiencies of…
This paper introduces a variant of the impartial combinatorial game nim, called tree nim, as well as a particular case of tree nim called tripod nim. A certain existence-uniqueness result and a periodicity result are proven about the…
We present tropical games, a generalization of combinatorial min-max games based on tropical algebras. Our model breaks the traditional symmetry of rational zero-sum games where players have exactly opposed goals (min vs. max), is more…
Efficient implementations of sets and maps (dictionaries) are important in computer science, and balanced binary search trees are the basis of the best practical implementations. Pedagogically, however, they are often quite complicated,…
We study the complexity of several combinatorial problems in the model of binary networked public goods games. In this game, players are represented by vertices in a network, and the action of each player can be either investing or not…