Matches in SemOpenAlex for { <https://semopenalex.org/work/W2079479907> ?p ?o ?g. }
Showing items 1 to 93 of
93
with 100 items per page.
- W2079479907 abstract "Two of the pillars of combinatorics are the notion of choosing an arbitrary subset of a set with $n$ elements (which can be done in $2^n$ ways), and the notion of choosing a $k$-element subset of a set with $n$ elements (which can be done in $n choose k$ ways). In this article I sketch the beginnings of a theory that would import these notions into the category of hedral sets in the sense of Morelli and the category of polyhedral sets in the sense of Schanuel. Both of these theories can be viewed as extensions of the theory of finite sets and mappings between finite sets, with the concept of cardinality being replaced by the more general notion of Euler measure (sometimes called combinatorial Euler characteristic). I prove a ``functoriality'' theorem (Theorem 1) for subset-selection in the context of polyhedral sets, which provides quasi-combinatorial interpretations of assertions such as $2^{-1} = frac12$ and ${1/2 choose 2} = -frac18$. Furthermore, the operation of forming a power set can be viewed as a special case of the operation of forming the set of all mappings from one set to another; I conclude the article with a polyhedral analogue of the set of all mappings between two finite sets, and a restrictive but suggestive result (Theorem 2) that offers a hint of what a general theory of exponentiation in the polyhedral category might look like." @default.
- W2079479907 created "2016-06-24" @default.
- W2079479907 creator A5032538374 @default.
- W2079479907 date "2002-03-30" @default.
- W2079479907 modified "2023-09-27" @default.
- W2079479907 title "Exponentiation and Euler measure" @default.
- W2079479907 cites W1481438721 @default.
- W2079479907 cites W1984499246 @default.
- W2079479907 cites W1991050933 @default.
- W2079479907 cites W2044240207 @default.
- W2079479907 cites W2064845646 @default.
- W2079479907 cites W938873559 @default.
- W2079479907 hasPublicationYear "2002" @default.
- W2079479907 type Work @default.
- W2079479907 sameAs 2079479907 @default.
- W2079479907 citedByCount "0" @default.
- W2079479907 crossrefType "posted-content" @default.
- W2079479907 hasAuthorship W2079479907A5032538374 @default.
- W2079479907 hasConcept C100643331 @default.
- W2079479907 hasConcept C11413529 @default.
- W2079479907 hasConcept C114614502 @default.
- W2079479907 hasConcept C118615104 @default.
- W2079479907 hasConcept C124101348 @default.
- W2079479907 hasConcept C134306372 @default.
- W2079479907 hasConcept C151730666 @default.
- W2079479907 hasConcept C153046414 @default.
- W2079479907 hasConcept C162392398 @default.
- W2079479907 hasConcept C177264268 @default.
- W2079479907 hasConcept C17744445 @default.
- W2079479907 hasConcept C199360897 @default.
- W2079479907 hasConcept C199539241 @default.
- W2079479907 hasConcept C200288055 @default.
- W2079479907 hasConcept C2779231336 @default.
- W2079479907 hasConcept C2779343474 @default.
- W2079479907 hasConcept C2780009758 @default.
- W2079479907 hasConcept C33923547 @default.
- W2079479907 hasConcept C41008148 @default.
- W2079479907 hasConcept C62884695 @default.
- W2079479907 hasConcept C77088390 @default.
- W2079479907 hasConcept C81539297 @default.
- W2079479907 hasConcept C86803240 @default.
- W2079479907 hasConcept C87117476 @default.
- W2079479907 hasConceptScore W2079479907C100643331 @default.
- W2079479907 hasConceptScore W2079479907C11413529 @default.
- W2079479907 hasConceptScore W2079479907C114614502 @default.
- W2079479907 hasConceptScore W2079479907C118615104 @default.
- W2079479907 hasConceptScore W2079479907C124101348 @default.
- W2079479907 hasConceptScore W2079479907C134306372 @default.
- W2079479907 hasConceptScore W2079479907C151730666 @default.
- W2079479907 hasConceptScore W2079479907C153046414 @default.
- W2079479907 hasConceptScore W2079479907C162392398 @default.
- W2079479907 hasConceptScore W2079479907C177264268 @default.
- W2079479907 hasConceptScore W2079479907C17744445 @default.
- W2079479907 hasConceptScore W2079479907C199360897 @default.
- W2079479907 hasConceptScore W2079479907C199539241 @default.
- W2079479907 hasConceptScore W2079479907C200288055 @default.
- W2079479907 hasConceptScore W2079479907C2779231336 @default.
- W2079479907 hasConceptScore W2079479907C2779343474 @default.
- W2079479907 hasConceptScore W2079479907C2780009758 @default.
- W2079479907 hasConceptScore W2079479907C33923547 @default.
- W2079479907 hasConceptScore W2079479907C41008148 @default.
- W2079479907 hasConceptScore W2079479907C62884695 @default.
- W2079479907 hasConceptScore W2079479907C77088390 @default.
- W2079479907 hasConceptScore W2079479907C81539297 @default.
- W2079479907 hasConceptScore W2079479907C86803240 @default.
- W2079479907 hasConceptScore W2079479907C87117476 @default.
- W2079479907 hasLocation W20794799071 @default.
- W2079479907 hasOpenAccess W2079479907 @default.
- W2079479907 hasPrimaryLocation W20794799071 @default.
- W2079479907 hasRelatedWork W1424698467 @default.
- W2079479907 hasRelatedWork W149310769 @default.
- W2079479907 hasRelatedWork W149671515 @default.
- W2079479907 hasRelatedWork W1971176787 @default.
- W2079479907 hasRelatedWork W2029181882 @default.
- W2079479907 hasRelatedWork W204859252 @default.
- W2079479907 hasRelatedWork W2050888701 @default.
- W2079479907 hasRelatedWork W2054245750 @default.
- W2079479907 hasRelatedWork W2107232728 @default.
- W2079479907 hasRelatedWork W2126565260 @default.
- W2079479907 hasRelatedWork W2136604612 @default.
- W2079479907 hasRelatedWork W2186289717 @default.
- W2079479907 hasRelatedWork W2330604690 @default.
- W2079479907 hasRelatedWork W2332328989 @default.
- W2079479907 hasRelatedWork W2476170865 @default.
- W2079479907 hasRelatedWork W2519197805 @default.
- W2079479907 hasRelatedWork W2767252625 @default.
- W2079479907 hasRelatedWork W2964222779 @default.
- W2079479907 hasRelatedWork W3046704607 @default.
- W2079479907 hasRelatedWork W3106086156 @default.
- W2079479907 isParatext "false" @default.
- W2079479907 isRetracted "false" @default.
- W2079479907 magId "2079479907" @default.
- W2079479907 workType "article" @default.