Shellability of relative squeezed balls and spheres

Squeezed balls and spheres, introduced by Kalai, form a rich class of triangulated complexes arising from subcomplexes of cyclic polytopes, with well-understood shellability properties.

Recently, Novik and Zheng introduced relative squeezed balls, obtained as differences of squeezed balls, and used them to construct large families of highly neighborly simplicial spheres.

While these complexes are known to be constructible, their shellability has remained open.

In this paper, we resolve this question by proving that both relative squeezed balls and their boundary complexes are shellable.

We provide explicit shelling orders and characterize restriction faces, thereby establishing strong combinatorial structure for this new class of complexes.