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comment Connected components $0-1$ matrices
@TheMaskedAvenger You could state your answer completely.
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revised Connected components $0-1$ matrices
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comment Connected components $0-1$ matrices
Sorry I thought I removed it in the mathoverflow post.
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revised Connected components $0-1$ matrices
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asked Connected components $0-1$ matrices
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revised Question on induction technique
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asked Question on induction technique
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accepted Polynomials of low degree that clone polynomials of higher degree
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comment Polynomials of low degree that clone polynomials of higher degree
Interesting.... let me read the article.
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comment Polynomials of low degree that clone polynomials of higher degree
Would the idea work if we had $(x_1+x_2-x_3+x_4)(x_5-x_6-x_7-x_8)(x_9+x_{10}-x_{11}-x_{12})(x_{13}-x_{14}+x_{15}+x_{16})$ (some terms have negative sign)?
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comment Limitations of techniques in communication complexity
@SureshVenkat can you please provide a reference? I am not sure about partition bound.
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comment Polynomials of low degree that clone polynomials of higher degree
nice answer I like it.
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comment Polynomials of low degree that clone polynomials of higher degree
Yeah you seem correct. My understanding was that $|S|\leq 3$ comes from the fact that $f=0$ if $3$ or less variables are set. It seems the same idea will work for both polynomials(for the first polynomial you can take $|S|\leq 5$ and for the second you can take $|S|\leq3$). But could you clarify the induction step further?
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comment Polynomials of low degree that clone polynomials of higher degree
Also the proof may not work if we had $$f(x_1,\dots,x_{24})=(x_1+x_2+x_3+x_4)(x_5+x_6+x_7+x_8)(x_9+x_{10}+x_{11}+x_{12­})(x_{13}+x_{14}+x_{15}+x_{16})(x_{17}+x_{19}+x_{19}+x_{20})(x_{21}+x_{22}+x_{23}­+x_{24})\in\Bbb R[x]$$ or $$f(x_1,\dots,x_{24})=(x_1+x_2+x_3+x_4+x_5+x_6)(x_7+x_8+x_9+x_{10}+x_{11}+x_{12}­)(x_{13}+x_{14}+x_{15}+x_{16}+x_{17}+x_{18})(x_{19}+x_{20}+x_{21}+x_{22}+x_{23}+x_­{24})\in\Bbb R[x]$$ correct?
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comment Polynomials of low degree that clone polynomials of higher degree
updated to clarify ring.
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comment Polynomials of low degree that clone polynomials of higher degree
@NoahStein I am not much familiar with wreath product. could you explicitly comment the action?
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revised Limitations of techniques in communication complexity
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