question about partitions

[N. J. A. Sloane]

Anyone want to help this correspondent?  -  njas



>>From mahmoud.bekheit at eee.strath.ac.uk  Thu Feb 14 10:12:33 2002
>>Delivered-To: njas at research.att.com
>>From: "Mahmoud Bekheit" <mahmoud.bekheit at eee.strath.ac.uk>
>>To: <njas at research.att.com>
>>Subject: Help: Partitions of a number into summand parts & Non-equivalent under rotation
>>Date: Thu, 14 Feb 2002 15:10:36 -0000
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>>Dear Prof. Sloane
>>
>>I'm interested in generating all partitions of an integer number n into
>>parts p, each partition should be permutated to five all possible prtts
>>permutations. This permutation should satisfy the "non-equivalent under
>>rotation", like Necklaces.
>>
>>e.g.
>>n=10, p=4
>>One possible partition is = 1, 2, 3, 4
>>the allowed permuations are
>>1 4 3 2
>>1 2 4 3
>>1 3 4 2
>>1 2 3 4
>>
>>To generate these sequence
>>a) I have to generate all Un;abeled binary Necklaces of n number of beads.
>>b) change the binary representation into runs of consecutive ones and
>>zeross. e.g. 111001100 = 3,2,2,2
>>c) selecting from all runs the ones that have certain number of runs (parts)
>>
>>sample results are:
>>
>>p          2        4        6        8        10
>>===================================
>>n
>>2          1
>>4          2        1
>>6          3        3        1
>>8          4        10      4        1
>>10        5        22      22      5        1
>>12        6        43      80      43      6      1
>>14        7        73      217    217    73    7     1
>>16        8        116    504    810    504  116        1
>>
>>My question to you
>>Is there any definition of this sequence(non equivalent under rotation for
>>set of p parts)
>>
>>Thanks
>>Mahmoud Bekheit
>>University of Strathclyde
>>Department of Electronic and Electrical Engineering
>>Royal College Building
>>204 George Street
>>Glasgow G1 1XW
>>Scotland, U.K
>>
>>Tel: 0141 548 2544
>>Int.: +44 141 548 2544
>>Fax: 0141 552 2487
>>E-mail: mahmoud.bekheit at eee.strath.ac.uk
>>