OddPartsWord from IntegerPartition

The binary word marking which parts are odd, the parts taken largest first.

IntegerPartition → BinaryWord

FindStat's Mp00317. Lossy: only the parts' parity is kept.

Called as CombinatorialMap(x, "OddPartsWord"). The head's page has its examples.

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Each element of IntegerPartition at a size, and its image, applied in your browser; sizes past 7 are not offered.

Size

Properties

Sizes 1 to

Transport a statistic

Pick a statistic on BinaryWord. Its distribution over the images of IntegerPartition at each size is computed, and compared with the 165 statistics on IntegerPartition: those that share it are the ones the map sends it to, as far as the sizes computed show.

Statistic Sizes 1 to

FindStat Mp00317

odd parts

Matched by value: our map agrees with FindStat's image on each of the 29 rows of size at most 6 we can read (0 unread; its table has 1200 rows).

Surjectionas FindStat records them, checked by FindStat's contributors.

Return the binary word indicating which parts of the partition are odd.

Object	Image
`[1]`	`1`
`[2]`	`0`
`[3]`	`1`
`[4]`	`0`

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/Mp00317 has the rest.