论文信息 - Some properties of crossings and partitions

Some properties of crossings and partitions

We give a group theoretical interpretation of the lattice of non-crossing partitions of a cycle of length m. Using this interpretation, we prove that the group of skew-automorphisms of this lattice is isomorphic to the dihedral group D4m. We also give some generating functions, in terms of continued fraction expansions, for some statistics on the set of partitions involving the number of restricted crossings and the number of classes.

Philippe Biane | P. Biane

[1] Paul H. Edelman. Chain enumeration and non-crossing partitions , 1980, Discret. Math..

[2] P. Biane. Permutation model for semi-circular systems and quantum random walks , 1995 .

[3] R. Speicher. A new example of ‘independence’ and ‘white noise’ , 1990 .

[4] Germain Kreweras,et al. Sur les partitions non croisees d'un cycle , 1972, Discret. Math..

[5] A. Nica. R-Transforms of Free Joint Distributions and Non-crossing Partitions , 1996 .

[6] Philippe Biane,et al. Permutations following excess type and number of inversions and combinatory interpretation of a continued fraction of Heine , 1993 .

[7] Roland Speicher,et al. An example of a generalized Brownian motion , 1991 .

[8] Philippe Biane,et al. Permutations Suivant le Type d'Exce'dance et le Nombre d'Inversions et Interpre'tation Combinatoire d'une Fraction Continue de Heine , 1993, Eur. J. Comb..

[9] Paul H. EDELMAN. Multichains, non-crossing partitions and trees , 1982, Discret. Math..

[10] Rodica Simion,et al. On the structure of the lattice of noncrossing partitions , 1991, Discret. Math..

[11] Philippe Flajolet. Combinatorial aspects of continued fractions , 1980, Discret. Math..

[12] R. Speicher. Multiplicative functions on the lattice of non-crossing partitions and free convolution , 1994 .