  Recently, Blecher and Knopfmacher explored the notion of fixed points in
integer partitions. Here, we distinguish partitions with a fixed point by which
value is fixed and analyze the resulting triangle of integers. In particular,
we confirm various identities for diagonal sums, row sums, and antidiagonal
sums (which are finite for this triangle) and establish a four-term recurrence
for triangle entries analogous to Pascal's lemma for the triangle of binomial
coefficients. The partition statistics crank and mex arise. All proofs are
combinatorial.
