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In mathematics, a locally finite poset is a partially ordered set ''P'' such that for all ''x'', ''y'' ∈ ''P'', the interval () consists of finitely many elements. Given a locally finite poset ''P'' we can define its ''incidence algebra''. Elements of the incidence algebra are functions ''ƒ'' that assign to each interval () of ''P'' a real number ''ƒ''(''x'', ''y''). These functions form an associative algebra with a product defined by : There is also a definition of ''incidence coalgebra''. In theoretical physics a locally finite poset is also called a causal set and has been used as a model for spacetime. ==References== Stanley, Richard P. Enumerative Combinatorics, Volume I. Cambridge University Press, 1997. Pages 98, 113—116. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「locally finite poset」の詳細全文を読む スポンサード リンク
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