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The update statistic can be triggered per partition when the number of modification reaches the threshold value = (total rows / number of partitions) * 20%. In my case the big Transactionhistory table contains 46895292 rows.
Besides, adding a new partition that does not modify more than 20% of the total rows will not issue an automatic update statistic operation and no information about it will not be available.
Fortunately incremental statistics changes the story here.
We used SQL Server 2005 and we already faced to some challenges like statistics updates.
Database administrators who use partitioning with version older than SQL Server 2014 know what I mean.
We can use the new internal dynamic management function to figure out how statistic pages are organized with incremental statistics.