/usr/include/trilinos/ is in libtrilinos-pike-dev 12.10.1-3.
This file is owned by root:root, with mode 0o755.
..
/usr/include/trilinos/Makefile.export.Pike
/usr/include/trilinos/Makefile.export.PikeBlackBox
/usr/include/trilinos/Makefile.export.PikeImplicit
/usr/include/trilinos/Pike_BlackBoxModelEvaluator.hpp
/usr/include/trilinos/Pike_BlackBoxModelEvaluator_Logger.hpp
/usr/include/trilinos/Pike_BlackBoxModelEvaluator_SolverAdapter.hpp
/usr/include/trilinos/Pike_BlackBox_config.hpp
/usr/include/trilinos/Pike_DataTransfer.hpp
/usr/include/trilinos/Pike_DataTransfer_Logger.hpp
/usr/include/trilinos/Pike_MultiphysicsDistributor.hpp
/usr/include/trilinos/Pike_Solver.hpp
/usr/include/trilinos/Pike_SolverObserver.hpp
/usr/include/trilinos/Pike_SolverObserver_DefaultBase.hpp
/usr/include/trilinos/Pike_SolverObserver_Logger.hpp
/usr/include/trilinos/Pike_Solver_AbstractFactory.hpp
/usr/include/trilinos/Pike_Solver_BlockGaussSeidel.hpp
/usr/include/trilinos/Pike_Solver_BlockJacobi.hpp
/usr/include/trilinos/Pike_Solver_DefaultBase.hpp
/usr/include/trilinos/Pike_Solver_Factory.hpp
/usr/include/trilinos/Pike_Solver_TransientStepper.hpp
/usr/include/trilinos/Pike_StatusTest.hpp
/usr/include/trilinos/Pike_StatusTest_AbstractFactory.hpp
/usr/include/trilinos/Pike_StatusTest_Composite.hpp
/usr/include/trilinos/Pike_StatusTest_Factory.hpp
/usr/include/trilinos/Pike_StatusTest_GlobalModelConvergence.hpp
/usr/include/trilinos/Pike_StatusTest_LocalModelConvergence.hpp
/usr/include/trilinos/Pike_StatusTest_LocalModelFailure.hpp
/usr/include/trilinos/Pike_StatusTest_MaxIterations.hpp
/usr/include/trilinos/Pike_StatusTest_ScalarResponseRelativeTolerance.hpp