Timeline for Combinatorial Morse functions and random permutations
Current License: CC BY-SA 3.0
23 events
| when toggle format | what | by | license | comment | |
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| Jul 9, 2014 at 16:27 | answer | added | Ira Gessel | timeline score: 16 | |
| Nov 20, 2012 at 21:44 | vote | accept | Liviu Nicolaescu | ||
| Nov 20, 2012 at 20:07 | answer | added | John Shareshian | timeline score: 4 | |
| Nov 20, 2012 at 17:10 | answer | added | Richard Stanley | timeline score: 12 | |
| Nov 20, 2012 at 12:06 | vote | accept | Liviu Nicolaescu | ||
| Nov 20, 2012 at 21:43 | |||||
| Nov 20, 2012 at 3:33 | answer | added | Bruce Sagan | timeline score: 10 | |
| Nov 19, 2012 at 21:39 | comment | added | Liviu Nicolaescu | @ Patricia: Thanks for the added tag. | |
| Nov 19, 2012 at 20:35 | comment | added | Patricia Hersh | @Liviu: I like your question and have been meaning to think about it for some time now, but never seem to have the time. Meanwhile, I hope you don't mind that I added an enumerative-combinatorics tag to it, in case that might draw some additional other people's attention to your question. It seemed to me at least like an interesting relaxation of counting alternating permutations. | |
| Nov 19, 2012 at 16:46 | history | edited | Patricia Hersh |
edited tags
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| Feb 9, 2012 at 17:32 | history | edited | Liviu Nicolaescu | CC BY-SA 3.0 |
corrected spelling
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| Jan 20, 2012 at 21:49 | answer | added | Vidit Nanda | timeline score: 1 | |
| Jan 20, 2012 at 17:01 | history | edited | Liviu Nicolaescu | CC BY-SA 3.0 |
clarified exposition.
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| Jan 20, 2012 at 16:55 | history | edited | Liviu Nicolaescu | CC BY-SA 3.0 |
clarified a statement
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| Jan 20, 2012 at 16:47 | comment | added | Liviu Nicolaescu | @ Benjamin Steinberg: Thanks for point out Ken Brown's contribution. I was not aware. @ John Mangual: True. | |
| Jan 20, 2012 at 16:08 | answer | added | Karl Waugh | timeline score: 4 | |
| Jan 20, 2012 at 15:39 | comment | added | john mangual | @Liviu, okay so it's easy to find morse functions theoretically, but maybe not so easy to compute their critical points unless the space is very symmetric or the functions are well chosen. | |
| Jan 20, 2012 at 15:15 | comment | added | Benjamin Steinberg | Actually, discrete Morse theory was invented in the mid-80s by Ken Brown. He calls the notion a collapsing scheme on his paper on rewriting systems and monoid cohomplogy but it is equivalent to the acyclic matching formulation of Forman's theory. | |
| Jan 20, 2012 at 13:07 | comment | added | Liviu Nicolaescu | The hard problem is finding an embedding of the manifold $M$ in an Euclidean space $\mathbb{R}^N$, i.e., $N$ smooth functions $f_1,\dotsc, f_N: M\to\mathbb{R}$ which together define the embedding. Once you do that consider a linear combination $c_1f_1+\cdots +c_Nf_N$. Think of $c_1,\dotsc, c_n$ as i.i.d. Gaussian variables. Use a random number generator to assign values to these variables. Unless you are extremely unlucky, the resulting function will be Morse. | |
| Jan 20, 2012 at 12:24 | comment | added | john mangual | smooth morse functions made be a dime a dozon but hard to write down a specific one. | |
| Jan 20, 2012 at 12:06 | comment | added | Liviu Nicolaescu | Ooops! Thanks for point out the error. I meant $p_n\to 0$. I have corrected the typo. | |
| Jan 20, 2012 at 12:05 | history | edited | Liviu Nicolaescu | CC BY-SA 3.0 |
fixed glaring typo
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| Jan 20, 2012 at 10:52 | comment | added | Gerry Myerson | What did you mean to write when you wrote $p_n\to\infty$? | |
| Jan 20, 2012 at 10:39 | history | asked | Liviu Nicolaescu | CC BY-SA 3.0 |