The hypotheses of Lemma 18 on page 39 refer to a sequence using
set notation. The hypotheses should omit those set braces. The conclusion is correct as written, since that refers to a simplex. Here is a picture of a correction: |

The wording in Theorem 32 and subsequent "Clarifying
Observation" on page 65 might be misleading. The theorem is not asserting that every maximal chain contains at least
n-1 elements,merely that there are at least (n-1)! chains that do so. Here is a picture of a
rewording: |