SmirnovWordCount on IntegerPartition
The words with each letter used this many times and no letter twice in a row: the Carlitz-Scoville-Vaughan sum over the numbers of runs of each letter, taken as a binomial convolution over the parts.
FindStat's St001097 reads it as a coefficient of the formal group law for linear orders; its description gives the Smirnov words.
Called as CombinatorialStat(x, "SmirnovWordCount"). The head's page has its examples.
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Distribution
Over IntegerPartitions at each size, tallied here in your browser; sizes past 30 are not offered.
FindStat St001097
The coefficient of the monomial symmetric function indexed by the partition in the formal group law for linear orders.
| Object | Value |
|---|---|
[2] | 0 |
[3] | 0 |
[4] | 0 |
[5] | 0 |
[6] | 0 |
[7] | 0 |
[8] | 0 |
[9] | 0 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001097 has the rest.