Unformatted text preview: n vertices. There is a completely diFerent approach to this enumeration problem. Use the Expo-nential ±ormula to compute the exponential generating function for labeled, connected graphs. 4 Give a probabilistic proof that as n tends to in²nity, the proportion of labeled graphs on n vertices which are connected tends to 1. 5 The inversion graph of the permutation π of length n , denoted G π , is the graph on [ n ] where i ∼ j if and only if i < j and π ( i ) > π ( j ). ±or which permutations π is G π a path? 6 Prove that the growth rate of Av( k ··· 21) is ( k-1) 2 . (We will discuss growth rates on Monday, 4/11.)...
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- Spring '11
- Combinatorics, exponential generating function, take-home final project, set partition lattice