Combinatorial representations
نویسندگان
چکیده
منابع مشابه
Combinatorial representations
This paper introduces combinatorial representations, which generalise the notion of linear representations of matroids. We show that any family of subsets of the same cardinality has a combinatorial representation via matrices. We then prove that any graph is representable over all alphabets of size larger than some number depending on the graph. We also provide a characterisation of families r...
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Combinatorial auctions (CAs) are an important mechanism for allocating multiple goods while allowing self-interested agents to specify preferences over bundles of items. Winner determination for a CA is known to be NP-complete. However, restricting the problem can allow us to solve winner determination in polynomial time. These restrictions sometimes apply to the CA’s representation. There are ...
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Given a category C of a combinatorial nature, we study the following fundamental question: how does the combinatorial behavior of C affect the algebraic behavior of representations of C? We prove two general results. The first gives a combinatorial criterion for representations of C to admit a theory of Gröbner bases. From this, we obtain a criterion for noetherianity of representations. The se...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2013
ISSN: 0097-3165
DOI: 10.1016/j.jcta.2012.12.002