In the 1990s, Stanley and Brenti developed the foundations of what is now known as the Kazhdan--Lusztig--Stanley (KLS) theory. To each kernel in a graded poset, one may associate special functions called KLS polynomials. This framework unifies and puts a common ground for i) the Kazhdan--Lusztig polynomial of a Bruhat interval in a Coxeter group, ii) the toric g-polynomial of a polytope, iii) the Kazhdan-Lusztig polynomial of a matroid. In this talk I will introduce a new family of functions, called Chow functions, that encode various deep cohomological aspects of the combinatorial objects named before. In the three settings mentioned before, the Chow function describes i) a descent-like statistic enumerator for paths in the Bruhat graph, ii) the enumeration of chains of faces of the polytope, iii) the Hilbert series of the matroid Chow ring. This is joint work with Jacob P. Matherne and Lorenzo Vecchi. -- This seminar is part of the activities of the Dipartimento di Eccellenza CUP B83C23001390001 and it is funded by the European Union – Next Generation EU.