An Algorithm to Compute the Möbius Function of the Rotation Lattice of Binary Trees

Bien que le treillis de rotation des arbres binaires ne soit pas modulaire, on montre que sa fonction de Mobius μ se calcule de la meme maniere que pour les treillis distributifs. Si T et T' sont deux arbres binaires a n nœud internes, on exhibe un algorithme de complexite O(n 3/2 ) en temps et O(n) en espace pour calculer μ(T, T')

[1]  G. Grätzer General Lattice Theory , 1978 .

[2]  R. Tarjan,et al.  Rotation distance, triangulations, and hyperbolic geometry , 1986, STOC '86.

[3]  Samuel Huang,et al.  Problems of Associativity: A Simple Proof for the Lattice Property of Systems Ordered by a Semi-associative Law , 1972, J. Comb. Theory, Ser. A.

[4]  Jean Marcel Pallo,et al.  On the Rotation Distance in the Lattice of Binary Trees , 1987, Inf. Process. Lett..

[5]  Jean Marcel Pallo,et al.  A Distance Metric on Binary Trees Using Lattice-Theoretic Measures , 1990, Inf. Process. Lett..

[6]  Dov Tamari,et al.  Problèmes d'associativité: Une structure de treillis finis induite par une loi demi-associative , 1967 .

[7]  G. Rota On the foundations of combinatorial theory I. Theory of Möbius Functions , 1964 .

[8]  P. Hall,et al.  THE EULERIAN FUNCTIONS OF A GROUP , 1936 .

[9]  Feller William,et al.  An Introduction To Probability Theory And Its Applications , 1950 .

[10]  B. Monjardet,et al.  Finite pseudocomplemented lattices , 1992 .

[11]  Curtis Greene,et al.  The Möbius Function of a Partially Ordered Set , 1982 .

[12]  George Markowsky,et al.  The factorization and representation of lattices , 1975 .

[13]  Numérisation de documents anciens mathématiques Informatique théorique et applications : Theoretical informatics and applications. , 1986 .

[14]  Jean Marcel Pallo,et al.  Enumerating, Ranking and Unranking Binary Trees , 1986, Comput. J..

[15]  Robert E. Tarjan,et al.  Rotation distance, triangulations, and hyperbolic geometry , 1986, STOC '86.

[16]  Jean Marcel Pallo Some Properties of the Rotation Lattice of Binary Trees , 1988, Comput. J..

[17]  Mary Katherine Bennett,et al.  Two families of Newman lattices , 1994 .

[18]  Jean Marcel Pallo,et al.  A-transformation dans les arbres n-aires , 1983, Discret. Math..