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Partition representations: Difference between revisions
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Partition representations (view source)
Revision as of 14:59, 28 January 2020
, 14:59, 28 January 2020→Target indices: Lists of target indices are in bijection with partitions, not divisions
m (half a dozen "partition" → "division" changes according to definition above although that on line 69 may be contentious) |
m (→Target indices: Lists of target indices are in bijection with partitions, not divisions) |
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0 2 0 4 0 0 1 | 0 2 0 4 0 0 1 | ||
</source> | </source> | ||
This conversion can be used to show that like the other two representations, target indices represent | This conversion can be used to show that like the other two representations, target indices represent partitions bijectively. However, there is a concern regarding the final element, which is used to find the length of the division length vector above, that is, the number of divisions. If the target indices correspond exactly to the elements of the partitioned vector, then the last target index is the index of the last ''non-empty'' division. However, it is valid in a partition to include empty divisions at the end. In order to represent such divisions, we must allow an additional index after the last element of the partitioned vector. | ||
=== Divider counts === | === Divider counts === | ||