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Master's Dissertation
DOI
https://doi.org/10.11606/D.45.2020.tde-11082020-172703
Document
Author
Full name
Kayo Douglas da Silva
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2020
Supervisor
Committee
Abadi, Miguel Natalio (President)
Lambert, Rodrigo
Rousseau, Jerome François Alain Jean
Title in Portuguese
O problema generalizado do dominó
Keywords in Portuguese
Máximo encaixe
Sobreposição
Tempo de chegada
Abstract in Portuguese
Em um jogo de dominó clássico, com 7 símbolos possíveis e 2 símbolos por peça, qual a probabilidade de que duas peças escolhidas ao acaso e sem reposição se encaixem? A resolução desse problema prevê separar o conjunto de peças entre aquelas que possuem dois símbolos iguais (chamaremos de simétricas) e as que possuem símbolos distintos (não-simétricas) e calcular a probabilidade em cada caso. Numa generalização do problema, temos uma quantidade a de símbolos possíveis tomados de um conjunto finito A qualquer e peças constituídas já não de 2, mas de n símbolos tomados desse conjunto. Estamos interessados em encontrar, dadas duas peças escolhidas sem reposição, o tamanho máximo do encaixe entre elas.
Title in English
The generalized domino problem
Keywords in English
Hitting times
Maximal fitting
Overlap
Abstract in English
In a classic domino game with 7 possible symbols and 2 of them per piece, what is the probability that two randomly chosen pieces without replacement will fit together? The solution to this problem requires to separate the set of pieces between those that have two equal symbols (we will call them symmetrical) and those that have different ones (non-symmetrical) and calculate the probability in each case. In a generalization of the problem, we have a quantity a of possible symbols taken from any finite set A and pieces no longer consisting of 2 but n symbols taken from that set. We are interested in finding, given two pieces chosen without replacement, the maximum fitting size between them.
 
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Publishing Date
2021-03-02
 
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