Timeline for What's the volume of $\{x\in[0,1]^n|\sum x_i\le t\}$ for real $t$?
Current License: CC BY-SA 3.0
13 events
| when toggle format | what | by | license | comment | |
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| Nov 28, 2014 at 14:06 | comment | added | Pietro Majer | (On a side note, there is a principle of inclusion and exclusion, also related with processes of integration, even in Anthropology and Social Sciences. I believe that it shows in MO not less than its mathematical cousin) | |
| Nov 28, 2014 at 12:13 | comment | added | Pietro Majer | (If I had to name it only once or twice in a paper, I'd use the extended form. If I had to use it ten times in a page, I'd use the acronym, possibly clarifying it the first time. I guess that's what everybody does with every phrase to be repeated). | |
| Nov 28, 2014 at 8:56 | vote | accept | Mathieu Baillif | ||
| Nov 28, 2014 at 5:00 | comment | added | fedja | @KConrad Who knows? Usually the guys you are thinking of call it "sieve methods" and other fancy names specific to the particular branches of math. they are doing, but I would certainly refer to it as PIE myself if I ever needed to apply it in one of my own papers. :-) | |
| Nov 28, 2014 at 4:05 | comment | added | KConrad | @fedja: After posting my previous comment I had found PIE on the Art of Problem Solving website. Is it used by anyone in research papers, where abbreviations like PID, UFD, and DVR are common? | |
| Nov 28, 2014 at 3:18 | comment | added | Kevin O'Bryant | This is the Irwin-Hall distribution. | |
| Nov 28, 2014 at 3:16 | comment | added | fedja | @KConrad Almost every English-speaking school kid who took part in some math olympiads would call it this way. Just go to AoPS and check if you do not want to take my word for it :-). | |
| Nov 28, 2014 at 2:00 | comment | added | Pietro Majer | btw, I also use PIE as short form of my personal name. | |
| Nov 28, 2014 at 1:58 | comment | added | Pietro Majer | Yes, as soon as I finished texting it occurred to me there is this more geometrical and more elementary interpretation: write the characteristic function of the cube as a convenient linear combination of $[0,+\infty)^n$ and its translates, then integrating over $\sum_j x_j\le t$. | |
| Nov 28, 2014 at 1:52 | comment | added | KConrad | When I was a school kid, PIE was something to eat. Later when I took linguisitcs PIE was Proto-Indo-European. I don't think I've seen PIE as an abbreviation for the principle of inclusion-exclusion before. In what areas of math is that abbreviation widely used? | |
| Nov 28, 2014 at 1:46 | comment | added | fedja | Which, in the language of a school kid, is just PIE: take the simplex $S=\{x_i>0, \sum x_i<t\}$ and its translates $S_j$ by $n$ unit vectors. We want $v(S\setminus\cup (S\cap S_j)$ and the volumes of $S\cap (S_{j_1}\cap\dots\cap S_{j_k})$ are exactly $\frac 1{n!}(t-k)_+^n$. | |
| Nov 28, 2014 at 1:05 | history | edited | Pietro Majer | CC BY-SA 3.0 |
added 2 characters in body
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| Nov 28, 2014 at 0:47 | history | answered | Pietro Majer | CC BY-SA 3.0 |