sci.math.research Google Group

Re: Request regarding counting algorithms in graph theory

henne...@web.cs.ndsu.nodak.edu (Mike) — Thu, 18 Mar 2010 16:30:01 UT

Does the algorithm involve actually generating the sets?
If so, the obvious thing to do is check each set of remaining
nodes to see if they induce a connected subgraph.

Re: 3^n - 2^n and relatives

he...@uni-kassel.de (Gottfried Helms) — Thu, 18 Mar 2010 16:30:01 UT

A couple of years ago I posted some discussion here which were
kindly considered by some posters here. It occured, that the
ideas, with which I connected my own 1-cycle-attempt in the
collatz-problem with the approximation of |S*log2 - N*log3| were
essentially the same as that of Ray Steiner (and later John

Re: Request regarding counting algorithms in graph theory

chenr...@monmouth.com (Christopher Henrich) — Thu, 18 Mar 2010 16:30:01 UT

In article <hnqlgq$5b...@news.acm.uiuc.ed u>,
I misunderstood Knuth's example: it counts sets of edges which connect
the nodes of the graph.
But I think that an algorithm could be devised to count the partitions
of the nodes of the graph into two sets, each of which is connected by
arcs of the graph. I think the problems like this can be solved by means

Is there a not-easy-solvable PDE with probabilistic representation with known (or approximable) probability density?

andrewzak...@mail.ru (Andrew) — Wed, 17 Mar 2010 13:30:01 UT

It is well-known that solution of many equations could be represented
as expectation of some functional of random processes (e.g. Feynman�
Kac formula and etc.)
So the solution is the expectation which could be calculated by Monte-
Carlo method.
But if the probabilistic solution is the expectation of the random

Request regarding counting algorithms in graph theory

chenr...@monmouth.com (Christopher Henrich) — Wed, 17 Mar 2010 13:30:02 UT

Donald Knuth, in _The Art of Computer Programming_ Section 7.1.4 [1],
describes an algorithm for counting the connected sets of nodes in a
non-directed graph: see Exercise 55.
I am interested in a related problem, namely to count the partitions of
such a graph into two connected components. Are there any published

Call for papers XA2010

afor...@gmail.com (afortis@gmail.com) — Mon, 15 Mar 2010 13:40:50 UT

XA2010
"EUROPEAN CONFERENCE ON
COMPUTER SCIENCES & APPLICATIONS"
3rd Edition
Timi ?oara, Rom?nia, September 24-25, 2010
AIM
The 3rd European Conference on Computer Sciences and Applications
intends to stimulate the research activity and to establish
interactions between Romanian and foreign researchers, teachers, B.

Nine papers published by Geometry & Topology Publications

g...@msp.warwick.ac.uk (Geometry and Topology) — Sun, 14 Mar 2010 02:24:30 UT

Seven papers have been published by Algebraic & Geometric Topology
(1) Algebraic & Geometric Topology 10 (2010) 525-530
Faithfulness of a functor of Quillen
by William G Dwyer, Andrei Radulescu-Banu and Sebastian Thomas
URL: [link]
DOI: 10.2140/agt.2010.10.525

Re: decomposing rationals

henne...@web.cs.ndsu.nodak.edu (Mike) — Fri, 12 Mar 2010 22:06:54 UT

If a and b are rational,
this becomes an integer linear programming problem in two variables.
Such things are solvable in polynomial time.
I don't remember details.
I think that you can solve the linear relaxation
and plug away with Gomory fractional cuts.
Selecting the approximations could be tricky.

Re: minimum height of a 0-1 simplex

henne...@web.cs.ndsu.nodak.edu (Mike) — Fri, 12 Mar 2010 19:13:15 UT

The above is roughly 1/n, but there are worse examples:
e_j for j in 1..k
k
SUM e_j + e_L for L in k+1..n
j=1
k n
The vertices satisfy SUM x_j + (1-k) SUM x_j = 1
j=1 j=k+1
For k=2n/3, the distance to zero is roughly sqrt(27/(4n**3)).

Call for Papers Reminder (extended): The World Congress on Engineering WCE 2010

imecs_2...@iaeng.org (IMECS 2008) — Fri, 12 Mar 2010 10:42:22 UT

CFP: The World Congress on Engineering WCE 2010
WCE 2010: London, U.K., 30 June - 2 July, 2010
[link]
Draft Paper Submission Deadline (extended): 18 March, 2010
The WCE 2010 is organized by International Association of Engineers
(IAENG), a non-profit international association for the engineers and

Re: minimum height of a 0-1 simplex

henne...@web.cs.ndsu.nodak.edu (Mike) — Wed, 10 Mar 2010 19:48:09 UT

That is what I get, also.
The base satisfies the linear equation
n-1
SUM x[j] + (2-n)*x[n] = 1
j=1
Lower bound, anyone?

Re: minimum height of a 0-1 simplex

henne...@web.cs.ndsu.nodak.edu (Mike) — Wed, 10 Mar 2010 12:37:27 UT

I'm not sure what this means,
but I think that it is not true even in three dimension.
that a minimal-height-defining line segment of a
tetrahedron lies within the tetrahedron.
Consider a tetrahedron with the following vertices:
(0, 0, 0), (3, 2, 0), (3, -2, 0) and (4, 0, 1).
Its minimal-height-defining segment is (4, 0, 1)_(4, 0, 0).

Re: minimum height of a 0-1 simplex

corbenn...@googlemail.com (Corbennick) — Wed, 10 Mar 2010 12:37:27 UT

Yes, but it seems I made a mistake there, as the height-defining
segment
does not always lie inside the simplex.
However, it does so, if the simplex has the property that all angles
between
edges are at most \pi/2.
Now for a simplex with vertices in {0,1}^n this condition is
satisfied!
By symmetry, it is enough to check this at the vertex zero.

Re: minimum height of a 0-1 simplex

anton.deit...@googlemail.com (Anton) — Wed, 10 Mar 2010 12:37:29 UT

no, is not.
For example, consider the simplex spanned by zero, e=e_1+...+e_n, e_1,
e_2,...,e_{n-1},
where e_1,...,e_n is the standard basis.
A calculation shows that the vertex at zero has height equal to 1/
sqrt(n-1+(n-2)^2)
which for n>3 is less that 1/sqrt(n).

Whitehead Groups of Short Exact Sequence

wildstar...@hotmail.com (Jeffrey Rolland) — Wed, 10 Mar 2010 12:37:28 UT

Hello, all!
The Whitehead group of a group G, Wh(G), is a functor from the category
of (finitely presented?) groups to the category of Abelian groups. A
reference is _A Course in Simple Homotopy Theory_ by Cohen.
If I have a short exact sequence of finitely presented groups 1 -> K -> G
-> Q -> 1, and I take the Whitehead torsion of the sequence, forming Wh