Concepts inSecretary problems: weights and discounts
Secretary problem
The secretary problem is one of many names for a famous problem of the optimal stopping theory. The problem has been studied extensively in the fields of applied probability, statistics, and decision theory. It is also known as the marriage problem, the sultan's dowry problem, the fussy suitor problem, the googol game, and the best choice problem.
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Matroid
In combinatorics, a branch of mathematics, a matroid or independence structure is a structure that captures and generalizes the notion of linear independence in vector spaces. There are many equivalent ways to define a matroid, a phenomenon sometimes called cryptomorphism. Significant definitions of matroid include those in terms of independent sets, bases, circuits, closed sets or flats, closure operators, and rank functions.
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Family of sets
In set theory and related branches of mathematics, a collection F of subsets of a given set S is called a family of subsets of S, or a family of sets over S. More generally, a collection of any sets whatsoever is called a family of sets. The term "collection" is used here because, in some contexts, a family of sets may be allowed to contain repeated copies of any given member, and in other contexts it may form a proper class rather than a set.
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Function (mathematics)
In mathematics, a function is a relation between a set of inputs and a set of potential outputs with the property that each input is related to exactly one output. An example of such a relation is defined by the rule f(x) = x, which relates an input x to its square, which are both real numbers. The output of the function f corresponding to an input x is denoted by f(x) (read "f of x"). If the input is ¿3, then the output is 9, and we may write f(¿3) = 9.
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Mechanism design
Mechanism design (sometimes called reverse game theory) is a field in game theory studying solution concepts for a class of private information games. The distinguishing features of these games are: that a game "designer" chooses the game structure rather than inheriting one that the designer is interested in the game's outcome Such a game is called a "game of mechanism design" and is usually solved by motivating agents to disclose their private information.
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Bracket
Brackets are tall punctuation marks used in matched pairs within text, to set apart or interject other text. Used unqualified, brackets refer to different types of brackets in different parts of the world and in different contexts.
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Sequence
In mathematics, a sequence is an ordered list of objects (or events). Like a set, it contains members (also called elements), and the number of ordered element (possibly infinite) is called the length of the sequence. Unlike a set, order matters, and exactly the same elements can appear multiple times at different positions in the sequence. A sequence is a discrete function. For example, (C, R, Y) is a sequence of letters that differs from (Y, C, R), as the ordering matters.
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