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May 15 |
awarded | Commentator |
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May 15 |
comment |
Prove (without quoting any theorems) that polynomials on [0,1] are continous I don't understand the point of the first question. Shouldn't you replace $P([0, 1])$ by $C^0[0, 1]$ in this question? You can then combine both questions to show the desired result. (What your version of the first question asks you to prove is true but I fail to see where you will need to use it.) |
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May 14 |
awarded | Caucus |
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Feb 12 |
comment |
Width of a product of chains Thanks a lot for this detailed answer! Is this new, or are those results from an existing source? |
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Feb 11 |
revised |
Number of upper sets of size $n$ in a finite tree +terminology |
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Feb 10 |
comment |
Product-Decomposition of distributive lattices Related: mathoverflow.net/questions/97844/… |
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Feb 10 |
asked | Width of a product of chains |
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Feb 10 |
awarded | Critic |
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Feb 9 |
awarded | Teacher |
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Feb 9 |
revised |
Extending a partial order to antichains +isomorphic |
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Feb 9 |
answered | Extending a partial order to antichains |
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Feb 6 |
comment |
Number of upper sets of size $n$ in a finite tree Yes, you can indeed show by induction on the tree $T$ that $f_T$ is log-concave. Thanks a lot for pointing me to this, I believe this was the right notion needed for the induction hypothesis. If you edit your answer to mention this, I'll accept it. |
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Feb 4 |
comment |
Number of upper sets of size $n$ in a finite tree If it is indeed true that the convolution of two "mountains" is indeed a "mountains", then the result is proved and I'm happy, but in fact I'm not sure this is always true. |
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Feb 4 |
comment |
Number of upper sets of size $n$ in a finite tree Thanks for this remark. In fact, I'm already aware of the following result: for any binary tree $T$ with root subtrees $L$ and $R$ (not just the divisibility example you gave), we have $f_T(k) = \sum_i f_L(i) f_R(k-i-1)$. (Any upper set of size $i$ in $T$ is obtained by taking one upper set in $L$ and one in $R$, with all possible repartitions of sizes.) This generalizes to trees of arbitrary arity, and, indeed, it's a convolution. However, I can't manage to do an induction from here. I'm not sure if we don't need a stronger induction hypothesis that the result I conjectured. |
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Feb 4 |
revised |
Number of upper sets of size $n$ in a finite tree note about the link with partial orders |
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Feb 4 |
asked | Number of upper sets of size $n$ in a finite tree |
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Jan 30 |
revised |
How to understand the duality between Dilworth's theorem and Mirsky's theorem? edited tags |
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Jan 29 |
comment |
How to understand the duality between Dilworth's theorem and Mirsky's theorem? I'm interested in finite partial orders, I edited the question to reflect this. Thanks for this remark! |
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Jan 29 |
asked | How to understand the duality between Dilworth's theorem and Mirsky's theorem? |
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Jan 1 |
comment |
Extending a partial order to antichains WimC: A more detailed paper about the same thing by the same authors: isg.rhul.ac.uk/~jason/Pubs/imj.pdf |
