This compatibility chart provided by GNU appears to state that a GPLv3 program can include a LGPLv2.1-only library. This doesn't make sense to me as the LGPLv2.1 license would have to be compatible with GPLv3.
How is this combination possible?
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Actually, Section 3 of the LGPLv2.1 seems to be explain this quite clearly:
You may opt to apply the terms of the ordinary GNU General Public License instead of this License to a given copy of the Library. To do this, you must alter all the notices that refer to this License, so that they refer to the ordinary GNU General Public License, version 2, instead of to this License. (If a newer version than version 2 of the ordinary GNU General Public License has appeared, then you can specify that version instead if you wish.) Do not make any other change in these notices.