Matrices for binary relations? Fwd: TOPIC:Sequences

[Meeussen Wouter (bkarnd)]

sounds like Set Partitions and Bell Numbers.
The binary matrix looks like the non-attacking rooks picture of those Set Partitions.

BellList[1] = {{{1}}}; (* the basic case *)

BellList[n_Integer?Positive] := BellList[n] = (* do some caching *)
    Flatten[      Join[
        Map[ReplaceList[#,{S__}->{S,{n}}]&, BellList[n-1]],
        Map[ReplaceList[#,{b___,{S__},a___}->{b,{S,n},a}]&, BellList[n-1]]],
      1]

W.



-----Original Message-----
From: Antti Karttunen [mailto:antti.karttunen at gmail.com]
Sent: donderdag 24 november 2005 10:56
To: seqfan at ext.jussieu.fr; s040321 at student.dtu.dk
Subject: Matrices for binary relations? Fwd: TOPIC:Sequences



With Kristjan's permit, I'll post his question to the list:
If you reply, please include his address s040321 at student.dtu.dk
on the To:-line, as he is not a memeber of SeqFan-list.

---------- Forwarded message ----------
From: Kristjan Haukur Flosason <s040321 at student.dtu.dk>
Date: Nov 22, 2005 5:07 PM 
Subject: TOPIC:Sequences
To: antti.karttunen<#>gmail.com
 
Hi Antti,
I am working on my M.Sc. thesis in electrical engineering at DTU in Denmark and I got stuck in a combinatorial problem. I need to generate a number of alternative solutions that will later be examined for feasibility. Since I saw your name on the Encyclopedia of Integer Sequences, I thought you might have a hint for me. The problem formulation I am facing is the following:  
Given are n objects x1…xn and binary relational matrix FRij. The objects are to be assigned to slots where each slot can contain one or more objects. Two objects x i and xj can only exist in the same slot if their relation is given with FRij = 1. FRij = 1 does not force the objects into the same slot. How many alternative assignments are possible? 
Moreover: Which algorithm can be used to efficiently find all alternative assignments?  
Do you have a hint on how to approach a solution, where to find www resources or other hints?
Best regards,
--------------------------------
Kristján Haukur Flosason
stud.nr. s040321 

Ørsted-DTU, Automation
 - byg. 326, rum 117 -
DK 2800, Kgs. Lyngby
Mobile: 2964 3674
E-mail: s040321 at student.dtu.dk
--------------------------------

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