There are finitely many simplicial complexes (up to isomorphism) with a given number of vertices. Translating this fact to the language of $h$-vectors, there are finitely many simplicial complexes of bounded dimension with $h_1=k$ for any natural number $k$. In this paper we study the question at the other end of the $h$-vector: Are there only finitely many $(d-1)$-dimensional simplicial complexes with $h_d=k$ for any given $k$? The answer is no if we consider general complexes, but we focus on three cases coming from matroids: (i) independence complexes, (ii) broken circuit complexes, and (iii) order complexes of geometric lattices. Surprisingly, the answer is yes in all three cases.

具有给定数量的顶点的有限多个单纯形复形（直至同构）。将此事实翻译为$H$-向量，有有限个维的有限单纯形复 $H_{\mathrm{1个}}=ķ$ 对于任何自然数 $ķ$。在本文中，我们将研究另一端的问题$H$-vector：仅有限地存在 $（d-\mathrm{1个}）$维简单复形与 $H_d=ķ$ 对于任何给定 $ķ$？如果不考虑一般的复数，答案是否定的，但我们将重点放在来自类阵的三种情况：（i）独立复数，（ii）断路复数和（iii）几何格的阶数复数。令人惊讶的是，在所有三种情况下答案都是肯定的。