  In the paper, we focus on the silting properties and the combinatorial
properties of silting and Gorenstein, which is called Gorenstein silting, where
the main tools used are recollements of module categories and tensor products.
For a ring A and its idempotent ideal J, we show that an A/J-module T is a
silting A-module if and only if T is a silting A/J-module. For the finite
dimensional k-algebras, with k a field, we show that the tensor products of
silting modules are still silting. We also show that the (partial) Gorenstein
silting properties can be glued by the recollements of module categories of
Noetherian rings. As a consequence, we glue the Gorenstein silting modules of
an upper triangular matrix Gorenstein ring by those of the involved rings.
