  A chord diagram is a set of chords in which no pair of chords has a common
endvertex. For a chord diagram $E$ having a crossing $S = \{ ac, bd \}$, by the
chord expansion of $E$ with respect to $S$, we have two chord diagrams $E_1 =
(E\setminus S) \cup \{ ab, cd \}$ and $E_2 = (E\setminus S) \cup \{ da, bc \}$.
Starting from a chord diagram $E$, by iterating expansions, we have a binary
tree $T$ such that $E$ is a root of $T$ and a multiset of nonintersecting chord
diagrams appear in the set of leaves of $T$. The number of leaves, which is not
depending on the choice of expansions, is called the chord expansion number of
$E$. A $0$-$1$ Young diagram is a Young diagram having a value of $0$ or $1$
for all boxes. This paper shows that the chord expansion number of some type
counts the number of $0$-$1$ Young diagrams under some conditions. In
particular, it is shown that the chord expansion number of an $n$-crossing,
which corresponds to the Euler number, equals the number of $0$-$1$ Young
diagrams of shape $(n,n-1,\ldots,1)$ such that each column has at most one $1$
and each row has an even number of $1$'s.
