Lyndon words, permutations and trees
Christophe Hohlweg IRMA Christophe Reutenauer † Universit eduQu ebec a Montr eal
March 14, 2002
1 Introduction
A well-known combinatorial construction, that has many applications in Computer Science (Fran con (1976), Sedgewick and Flajolet (1996), Kundu (1977), Vuillemin (1980)), maps bijectively permutations in Sn onto binary, planary trees, with labels in 1,...,n , increasing from root to leaves; see { } Foata and Schutzen berger (1971), Donaghey (1975), Viennot (1976), Stanley (1986). This construction is illustrated in Figure 1; the inverse mapping is simply the projection.
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8 7 2 5 1 6 8 3 9 Figure 1