/usr/include/trilinos/ is in libtrilinos-trilinoscouplings-dev 12.10.1-3.
This file is owned by root:root, with mode 0o755.
..
/usr/include/trilinos/EpetraExt_AmesosAMDGlobal_CrsGraph.h
/usr/include/trilinos/EpetraExt_AmesosBTFGlobal_LinearProblem.h
/usr/include/trilinos/EpetraExt_AmesosBTF_CrsGraph.h
/usr/include/trilinos/EpetraExt_AmesosBTF_CrsMatrix.h
/usr/include/trilinos/EpetraExt_Isorropia_CrsGraph.h
/usr/include/trilinos/Ifpack_ML.h
/usr/include/trilinos/Makefile.export.TrilinosCouplings
/usr/include/trilinos/TrilinosCouplings_Version.h
/usr/include/trilinos/TrilinosCouplings_config.h
/usr/include/trilinos/nlnml_ConstrainedMultiLevelOperator.H
/usr/include/trilinos/nlnml_coarselevelnoxinterface.H
/usr/include/trilinos/nlnml_finelevelnoxinterface.H
/usr/include/trilinos/nlnml_linearsystem.H
/usr/include/trilinos/nlnml_nonlinearlevel.H
/usr/include/trilinos/nlnml_preconditioner.H
/usr/include/trilinos/nlnml_preconditioner_utils.H
/usr/include/trilinos/nlnml_prepostoperator.H