Samuel Vidal
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Registered User
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Feb 24 |
answered | Nth root of a matrix as an analytic function? |
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Feb 9 |
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Is the empty graph a tree? "disconnected" and "connected" not forming a dichotomy : brilliant, that's the point ! |
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Feb 9 |
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What is the cardinality of the family of unlabelled bipartite graphs on n vertices? thank you sir ! |
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Feb 5 |
answered | What is the cardinality of the family of unlabelled bipartite graphs on n vertices? |
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Feb 5 |
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What is the cardinality of the family of unlabelled bipartite graphs on n vertices? I've checked the combinatorial description which is ok (the isomorphisms of species) The computation is wrong and I 'm not sure how to do it right. There is a description of the functorial composition of species in the book on species but it is hard to work out. |
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Feb 3 |
revised |
What is the cardinality of the family of unlabelled bipartite graphs on n vertices? added 333 characters in body |
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Feb 3 |
answered | What is the cardinality of the family of unlabelled bipartite graphs on n vertices? |
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Feb 3 |
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Is the empty graph a tree? May be a way to clarify the question is to consider not the graph in itself but within its family. Consider The family (species) of connected graphs $G^c$ and the family of not necessarily connected graphs $G$. The relation between them is: $$G\simeq E(G^c)$$ where E stands for the species of sets. This natural isomorphism comes from existence and unicity of a decomposition of a graph (in $G$) in its connected components (in $G^c$). If you work out the details, $G^c$ can't have any graph of size zero. This is why you better not see the empty graph as connected. |
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Feb 1 |
revised |
Is the empty graph a tree? deleted 11 characters in body |
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Feb 1 |
answered | Is the empty graph a tree? |
