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WeakRecordPositionSum on IntegerComposition ​

The sum of the positions of the weak records.

On IntegerComposition

Knopfmacher and Mansour, Record statistics in integer compositions.

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

Live

Distribution

Over IntegerCompositions at each size, tallied here in your browser; sizes past 6 are not offered.

FindStat St000762

The sum of the positions of the weak records of an integer composition.

ObjectValue
[2]1
[3]1
[4]1
[5]1
[6]1
[7]1
[8]1
[9]1

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000762 has the rest.