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visits | member for | 10 months |
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stats | profile views | 271 |
Aug 28 |
revised |
Coloring graph such that the coloring classes are not maximal independent sets
added 95 characters in body |
Aug 28 |
answered | Coloring graph such that the coloring classes are not maximal independent sets |
Aug 23 |
comment |
Who defined and who coined “module”?
That 1927 Monthly article is also the online OED's earlist citation for this sense of "module". |
Aug 22 |
revised |
When does a hypergraph represent maximal independent sets?
added 7 characters in body |
Aug 22 |
answered | When does a hypergraph represent maximal independent sets? |
Aug 20 |
comment |
Is any axiom system for sets categorical?
But a countable model of set theory can be characterized up to isomorphism by a single first-order sentence of infinite length, right? |
Jul 31 |
comment |
Proofs of the uncountability of the reals.
Wouldn't it be simpler to work with surjections instead of injections? There is a surjection from $\mathcal P(\omega)$ to $\omega_1$, there is no surjection from $\omega$ to $\omega_1$, therefore $\mathcal P(\omega)$ is uncountable. |
Jul 16 |
answered | Is quasivariety generated by all perfect graphs finitely axiomatizable? |
Jul 16 |
comment |
Is quasivariety generated by all perfect graphs finitely axiomatizable?
If the class is axiomatizable by universal Horn sentences, and if it's finitely axiomatizable, then it's finitely axiomatizable by Horn sentences; this follows from the compactness theorem. However, the class of perfect graphs is not closed under direct product. Let $G$ be the graph obtained by adding one more edge to the cycle $C_5$.Then $G$ is perfect, but the direct product $G\times G$ is easily seen to contain $C_5$ as an induced subgraph. so it's not perfect. Many different products of graphs are considered in graph theory; maybe the theorem you cited is about some other graph product? |
Jul 15 |
revised |
Does the symmetric group on an infinite set have a minimal generating set?
added 209 characters in body |
Jul 15 |
revised |
Removal of non-isomorphic edges results in the same graph
corrected grammar |
Jul 15 |
suggested | suggested edit on Removal of non-isomorphic edges results in the same graph |
Jul 11 |
awarded | Nice Answer |
Jul 11 |
revised |
Does the symmetric group on an infinite set have a minimal generating set?
added 432 characters in body |
Jul 11 |
revised |
Does the symmetric group on an infinite set have a minimal generating set?
added 1 character in body |
Jul 11 |
revised |
Does the symmetric group on an infinite set have a minimal generating set?
added 3 characters in body |
Jul 11 |
revised |
Does the symmetric group on an infinite set have a minimal generating set?
corrected a typo |
Jul 11 |
comment |
Does the symmetric group on an infinite set have a minimal generating set?
@TheMaskedAvenger You may be right; I'm a newbie here and don't know much about the rules and culture of this site. I posted this with the idea that Jeremy Rickard might want to incorporate the argument into his answer to make it self-contained. |
Jul 11 |
comment |
Does the symmetric group on an infinite set have a minimal generating set?
@JeremyRickard I've copied out the proof of Galvin's Theorem 3.1 from a reprint of his paper, and posted it as a comment-disguised-as-an-answer. Hope I didn't make too many typos. |
Jul 11 |
answered | Does the symmetric group on an infinite set have a minimal generating set? |