When you set setSuppressDropDownArrow(false) for a DataValidation in a sheet of a XSSF-Workbook the DropDownArrows are NOT shown in the resulting Excel-File. The name of the method infers a different behavior. For a sheet of a HSSF-Workbook the DropDownArrows are shown. So in this case the behavior is correct.
Created attachment 31432 [details] A maven project depending on Apache POI 3.10-FINAL and demonstrating the issue.
Created attachment 31433 [details] A file generated with suppressdropdown = false but that still has no drop down arrow.
Created attachment 31434 [details] A file generated with suppressdropdown = true but that still has a drop down arrow.
I just attached examples of this bug. It still occurs in 3.10-FINAL. I checked out the code and couldn't understand why that happens: the code is crystal clear and should work as is. Maybe it's a serialization issue?