An isoperimetric inequality for the $s$-perimeter of sets was established by Frank and Seiringer (JFA, 2008). Whenever an isoperimetric inequality is known it is a natural question to ask whether an analogous result holds when the domains are restricted to the class of polygons (or polyhedra) with given number of sides (faces). In fact, Pólya and Szegő in their book (Princeton Univ. Press, 1951) discuss such analogues of the Faber–Krahn inequality and could only prove it in the case of triangular and quadrilateral domains. When the number of sides is $5$ or more it remains an open question. In this talk, I shall discuss some results obtained with Olivares–Contador for the $s$-fractional perimeter. This involves suitable generalizations of the ideas of Pólya and Szegő to the non-local setting.