## Show us your articles! Or what's your Erdos number?

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### Show us your articles! Or what's your Erdos number?

http://www.phil.uu.nl/preprints/ckipreprints/PREPRINTS/preprint056.pdf

Here it is.

Post your works too (if available)!

I hope this can lead to some productive collaborations. Well, maybe...

Stickied! - Spitvalve

Here it is.

Post your works too (if available)!

I hope this can lead to some productive collaborations. Well, maybe...

Stickied! - Spitvalve

From Russia with math.

- 3.14159265...
- Irrational (?)
**Posts:**2413**Joined:**Thu Jan 18, 2007 12:05 am UTC**Location:**Ajax, Canada

- cmacis
**Posts:**754**Joined:**Wed Dec 13, 2006 5:22 pm UTC**Location:**Leeds or Bradford, Thessex-
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We have mathmos here, just not a lot past the first year of BSc.

Saw the title and knew it would make no sense to me.

Saw the title and knew it would make no sense to me.

li te'o te'a vei pai pi'i ka'o ve'o su'i pa du li no

Mathematician is a function mapping tea onto theorems. Sadly this function is irreversible.

QED is Latin for small empty box.

Ceci nâ€™est pas une [s]pipe[/s] signature.

Mathematician is a function mapping tea onto theorems. Sadly this function is irreversible.

QED is Latin for small empty box.

Ceci nâ€™est pas une [s]pipe[/s] signature.

- FiddleMath
**Posts:**245**Joined:**Wed Oct 11, 2006 7:46 am UTC**Location:**Madison, WI-
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http://www.tehposse.org/matt/stuff/path_bundles.pdf

This might be a little more comprehensible, as it doesn't assume too much prior knowledge. On the other hand, it's a lot of details.

This might be a little more comprehensible, as it doesn't assume too much prior knowledge. On the other hand, it's a lot of details.

- EradicateIV
**Posts:**361**Joined:**Mon Mar 19, 2007 7:33 pm UTC**Location:**Brownsville, PA-
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- FiddleMath
**Posts:**245**Joined:**Wed Oct 11, 2006 7:46 am UTC**Location:**Madison, WI-
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http://www.dranger.com/iwsec06_co.pdf

Basically, it's a PSPACE reduction. In more depth, it proves an upper bound for the complexity of this one computer security model my prof created. I had to turn it into a graph problem and then... oh, it's just a big mess. I'm proud of this one because it got me Erdos 4.

- Mad Giraffe
**Posts:**102**Joined:**Thu May 03, 2007 1:20 am UTC**Location:**Drifting on a fleeting thought.-
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Ahw, these all look mighty interesting, but as usual I'm having a hard(er) time to understand because it is in english.

Drat.

And I'm not going to bother to upload my paper about the mathematics behind depth perception and how to calculate dimensions of a 3d object from a perspective view from 1 plane (My specialisation in maths was (tri)geometry) or 2 planes.

Because it is in dutch.

Not that interesting anyway.

Drat.

And I'm not going to bother to upload my paper about the mathematics behind depth perception and how to calculate dimensions of a 3d object from a perspective view from 1 plane (My specialisation in maths was (tri)geometry) or 2 planes.

Because it is in dutch.

Not that interesting anyway.

- adlaiff6
**Posts:**274**Joined:**Fri Nov 10, 2006 6:08 am UTC**Location:**Wouldn't you rather know how fast I'm going?-
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iw wrote:Link to my webspace 'cuz you have to buy the original:

http://www.dranger.com/iwsec06_co.pdf

Basically, it's a PSPACE reduction. In more depth, it proves an upper bound for the complexity of this one computer security model my prof created. I had to turn it into a graph problem and then... oh, it's just a big mess. I'm proud of this one because it got me Erdos 4.

I'll be Erdos 4 in (hopefully) another couple months.

adlaiff6 wrote:iw wrote:Link to my webspace 'cuz you have to buy the original:

http://www.dranger.com/iwsec06_co.pdf

Basically, it's a PSPACE reduction. In more depth, it proves an upper bound for the complexity of this one computer security model my prof created. I had to turn it into a graph problem and then... oh, it's just a big mess. I'm proud of this one because it got me Erdos 4.

I'll be Erdos 4 in (hopefully) another couple months.

Yeah, the only Erdos numbers that really count are 1 and 0. Otherwise, it basically just means you got a joint paper with someone reputable published (usually your adviser ).

- cmacis
**Posts:**754**Joined:**Wed Dec 13, 2006 5:22 pm UTC**Location:**Leeds or Bradford, Thessex-
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But there can be only one 0, also no more 1s are possible. If you hunt out the 1s you might get a 2.

li te'o te'a vei pai pi'i ka'o ve'o su'i pa du li no

Mathematician is a function mapping tea onto theorems. Sadly this function is irreversible.

QED is Latin for small empty box.

Ceci nâ€™est pas une [s]pipe[/s] signature.

Mathematician is a function mapping tea onto theorems. Sadly this function is irreversible.

QED is Latin for small empty box.

Ceci nâ€™est pas une [s]pipe[/s] signature.

FiddleMath wrote:http://www.tehposse.org/matt/stuff/path_bundles.pdf

This might be a little more comprehensible, as it doesn't assume too much prior knowledge. On the other hand, it's a lot of details.

Interesting stuff!

This might be the wrong thread to mention it, but your paper made me start thinking about words with more possible digits, so I played around with some ternary "path bundles" (obviously the definition had to be modified). It seems that analogues Lemma 1 and Lemma 2 hold for all p-ary path bundles (p a natural number), but I haven't tried it for higher p yet, and I certainly haven't proved the existence theorems!

Let a "path" be as before, but require that adjacent words differ only in one digit AND only by 1, with no wrap-around. So in base p=5, you have 0142~0132, but NOT 0142~0102.

Now specify that B(n,a,p) has p^a paths, and for each w in Qa whose digits include only 0 and p-1 (i.e. the true "vertices" of Qa), the bundle contains Pw such that

1. |Pw|=p^{n-a} (***<----EDIT: This line has been changed.***)

2. Pw(0)=0^{n-a}w

3. Pw(.)=(p-1)^{n-a}(w*) (***<----EDIT: This line has been changed.***)

4. Every word in Qn is in exactly one path

where w* is essentially treating the "p-1" digits as "1"s and taking the complement. So again in base 5, if you have w=4044, then w*=0400.

I THINK that this implies the following Lemmas (with proofs similar to those in your paper):

Lemma 1: B(n,a,p) exists only if n=1(mod p).

Lemma 2: If B(n,a,p) exists, then a <= n-log_p((p-1)n+1)

I could have made a mistake, though. And who knows whether these things ever exist; I haven't bothered to check even the simplest cases.

Last edited by Woxor on Wed May 09, 2007 2:19 am UTC, edited 4 times in total.

- FiddleMath
**Posts:**245**Joined:**Wed Oct 11, 2006 7:46 am UTC**Location:**Madison, WI-
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Woxor wrote:Lemma 1: B(n,a,p) exists only if n=1(mod p).

Lemma 2: If B(n,a,p) exists, then a <= n-log_p((p-1)n+1)

I could have made a mistake, though. And who knows whether these things ever exist; I haven't bothered to check even the simplest cases.

I've put a little thought into larger cubes; a lot of things that are simple for Q_n get much more complicated. In particular, n = 3, a = 0, p = 3 works; you can cover a 3x3x3 cube while with a path from 000 to 222, so your proposed generalized Lemma 1 doesn't hold.

[edit] It's been a while since I worked with this. [/edit]

Last edited by FiddleMath on Wed May 09, 2007 4:20 am UTC, edited 1 time in total.

FiddleMath wrote:I've put a little thought into larger cubes; a lot of things that are simple for Q_n get much more complicated. In particular, n = 3, a = 1, p = 3 works; you can cover a 3x3x3 cube while with a path from 000 to 222, so your proposed generalized Lemma 1 doesn't hold.

I probably misread something, but wouldn't B(3,1,3) need to include p^a=3^1=3 distinct paths, rather than just the one? I'll try to post my "proof" later on if I have time (otherwise it'll have to wait until Thursday or so).

EDIT: Also, my Rule 1 was totally wrong; I wrote 3^n, it should have been p^{n-a}. And Rule 3 had a "2" instead of a "p-1."

EDIT 2: Upon further reflection, I hadn't even considered the obvious fact that there are still only 2^n "true" vertices, so clearly that will influence the structure of the bundle. I'll have to think about whether my generalization even makes sense.

- FiddleMath
**Posts:**245**Joined:**Wed Oct 11, 2006 7:46 am UTC**Location:**Madison, WI-
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This paper, on the "100 prisoners and a lightbulb" problem, gets me an Erdős number of 4 :)

SpitValve wrote:I'm going to publish a condensed matter paper soon. Any idea how to link ErdÃ¶s to condensed matter physics?

I'm very tempted to call it "Madness? Blasphemy? This IS EPITAXY ON A (111) FCC PERIODIC SLAB OF LENNARD-JONESIUM" but it doesn't have a very good ring to it.

How about "This is Epitaxy. This is Epitaxy on a (111) FCC Periodic Slab of Lennard-Jonesium. Any Questions?"

- Torn Apart By Dingos
**Posts:**817**Joined:**Thu Aug 03, 2006 2:27 am UTC

- FiddleMath
**Posts:**245**Joined:**Wed Oct 11, 2006 7:46 am UTC**Location:**Madison, WI-
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Torn Apart By Dingos wrote:"This is my article on Epitaxy on a (111) FCC Periodic Slab of Lennard-Jonesium. There are many like it, but this one is mine."

We can make this colon-compliant pretty easily...

"This is my article on Epitaxy on a (111) FCC Periodic Slab of Lennard-Jonesium:

There are many like it, but this one is mine."

Mine references anti-drug commercials in the US during the 80s and the one after it refers to the Rifleman's Creed, which is famous from the movie Full Metal Jacket. I assume "colon compliance" means that every paper needs to have a colon in its title to be worth anything. Not sure though.SpitValve wrote:Maybe I'm just tired, but I don't think I got the jokes in the last 3 posts.

iw wrote:Mine references anti-drug commercials in the US during the 80s and the one after it refers to the Rifleman's Creed, which is famous from the movie Full Metal Jacket. I assume "colon compliance" means that every paper needs to have a colon in its title to be worth anything. Not sure though.

ic. Well, I was only in the US during the 80s for one day, and didn't watch any ads about drugs, as far as I recall. I haven't watched Full Metal Jacket (don't hurt me), but I kinda get the colon thing. w00t!

- 3.14159265...
- Irrational (?)
**Posts:**2413**Joined:**Thu Jan 18, 2007 12:05 am UTC**Location:**Ajax, Canada

- skeptical scientist
- closed-minded spiritualist
**Posts:**6139**Joined:**Tue Nov 28, 2006 6:09 am UTC**Location:**San Francisco

Does proofreading a book really count for Erdos number? I would think not.

I'm looking forward to the day when the SNES emulator on my computer works by emulating the elementary particles in an actual, physical box with Nintendo stamped on the side.

"With math, all things are possible." —Rebecca Watson

"With math, all things are possible." —Rebecca Watson

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