| dbo:abstract |
In mathematics, the mex of a subset of a well-ordered set is the smallest value from the whole set that does not belong to the subset. That is, it is the minimum value of the complement set. The name "mex" is shorthand for "minimum excluded" value. Beyond sets, subclasses of well-ordered classes have minimum excluded values. Minimum excluded values of subclasses of the ordinal numbers are used in combinatorial game theory to assign nim-values to impartial games.According to the Sprague–Grundy theorem, the nim-value of a game position is the minimum excluded value of the class of values of the positions that can be reached in a single move from the given position. Minimum excluded values are also used in graph theory, in greedy coloring algorithms. These algorithms typically choose an ordering of the vertices of a graph and choose a numbering of the available vertex colors. They then consider the vertices in order, for each vertex choosing its color to be the minimum excluded value of the set of colors already assigned to its neighbors. (en) mex (ang. minimum excluded) – dla danego zbioru złożonego z liczb porządkowych, najmniejsza liczba porządkowa, która do niego nie należy. Na przykład: gdzie to najmniejsza nieskończona (czyli typ porządkowy zbioru liczb naturalnych). W teorii Sprague-Grundy’ego mex odgrywa decydującą rolą w określaniu nimliczb. (pl) |
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dbr:Nim dbr:Limit_ordinal dbr:Class_(set_theory) dbr:Combinatorial_game_theory dbr:Subclass_(set_theory) dbc:Combinatorial_game_theory dbr:Nimber dbr:Graph_theory dbr:Sprague–Grundy_theorem dbr:Greedy_coloring dbr:Minimum dbr:Ordinal_number dbr:Impartial_game dbr:Normal_play_convention dbr:Subset dbr:Complement_set dbr:Nim-value dbr:Well-ordered |
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dbt:Math dbt:Reflist dbt:Mset |
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dbc:Combinatorial_game_theory |
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yago:WikicatOrdinalNumbers yago:Abstraction100002137 yago:DefiniteQuantity113576101 yago:Measure100033615 yago:Number113582013 yago:OrdinalNumber113597280 |
| rdfs:comment |
mex (ang. minimum excluded) – dla danego zbioru złożonego z liczb porządkowych, najmniejsza liczba porządkowa, która do niego nie należy. Na przykład: gdzie to najmniejsza nieskończona (czyli typ porządkowy zbioru liczb naturalnych). W teorii Sprague-Grundy’ego mex odgrywa decydującą rolą w określaniu nimliczb. (pl) In mathematics, the mex of a subset of a well-ordered set is the smallest value from the whole set that does not belong to the subset. That is, it is the minimum value of the complement set. The name "mex" is shorthand for "minimum excluded" value. (en) |
| rdfs:label |
Mex (mathematics) (en) Mex (pl) |
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