We use s(m,n) to denote the number of ways to seat m people at n circular tables with least one person at each table. The arrangements at any one table are not distinguished if one can be rotated into another (as in Example 1.16). The ordering of the tables is not taken into account. For instance, the arrangement in parts (a),(b),(c) of Fig.5.6 are considered the same; those in parts (a),(d),(e) are distinct (in pairs).
The number s (m,n) are referred to as the stirling numbers of the first kind.
a) If n > m, what is s(m, n)?
(b) For m > 1, what are s(m, m) and s(m, 1)?
(c) Determine s(m, m - 1) for m > 2.
(d) Show that for m > 3,
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