On 19/09/16 02:45, James A. Donald wrote:
On 9/12/2016 8:01 PM, Georgi Guninski wrote:
On Mon, Sep 12, 2016 at 07:50:50PM +1000, James A. Donald wrote:
To restate the problem:  Find a mapping between integers and injective
functions from N to X up to a permutation of N.

In this case, find a mapping between integers and an injective functions
from 18 to 36.

Sage (open source, sagemath.org) can do at least parts of what you
are asking.
Not sure I get the question about injective function, but AFAICT
treating the permutation as nonnegative integer in binary will do.

Example sage session:

sage: l=[0]*2+[1]*2
sage: pe=Permutations(l)
sage: pe.cardinality()
6
sage: pe[0]
[0, 0, 1, 1]
sage: for p in pe:  print p
[0, 0, 1, 1]
#...more




Found the the solution.

Combinatorial number system.

Suppose we have k cards, any one of which can be white or red, but which
are otherwise indistinguishable and interchangeable.

Combinatorial number system gives us a one to one mapping between
integers, and all possible subsets of an n element set.

Now I want a mapping between integers and all possible m element subsets
of an n element set, but for m approximating n/2 the mapping is dense
enough to be useful.

The mapping I described is a fully dense 1:1 bijective mapping between the 9075135300 possible ordered combinations of 18 zeros and 18 ones and the integers 0-9075135299.


If you didn't understand it, please ask, off- or on-list.

-- Peter F

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