MathDB
Miklos Schweitzer 1979_3

Source:

January 28, 2009
combinatorics proposedcombinatorics

Problem Statement

Let g(n,k) g(n,k) denote the number of strongly connected, <spanclass=′latex−italic′>simple</span> <span class='latex-italic'>simple</span> directed graphs with n n vertices and k k edges. (<spanclass=′latex−italic′>Simple</span> <span class='latex-italic'>Simple</span> means no loops or multiple edges.) Show that ∑k=nn2−n(−1)kg(n,k)=(n−1)!. \sum_{k=n}^{n^2-n}(-1)^kg(n,k)=(n-1)!. A. A. Schrijver
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