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seen Apr 15 at 14:40

May
15
awarded  Commentator
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.)
May
14
awarded  Caucus
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?
Feb
11
revised Number of upper sets of size $n$ in a finite tree
+terminology
Feb
10
comment Product-Decomposition of distributive lattices
Related: mathoverflow.net/questions/97844/…
Feb
10
asked Width of a product of chains
Feb
10
awarded  Critic
Feb
9
awarded  Teacher
Feb
9
revised Extending a partial order to antichains
+isomorphic
Feb
9
answered Extending a partial order to antichains
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.
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.
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.
Feb
4
revised Number of upper sets of size $n$ in a finite tree
note about the link with partial orders
Feb
4
asked Number of upper sets of size $n$ in a finite tree
Jan
30
revised How to understand the duality between Dilworth's theorem and Mirsky's theorem?
edited tags
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!
Jan
29
asked How to understand the duality between Dilworth's theorem and Mirsky's theorem?
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