Some properties of crossings and partitions

被引:105
作者
Biane, P [1 ]
机构
[1] UNIV PARIS 06,CNRS,PROBABIL LAB,F-75251 PARIS 05,FRANCE
关键词
D O I
10.1016/S0012-365X(96)00139-2
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
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 D-4m. 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.
引用
收藏
页码:41 / 53
页数:13
相关论文
共 11 条
[1]   Permutation model for semi-circular systems and quantum random walks [J].
Biane, P .
PACIFIC JOURNAL OF MATHEMATICS, 1995, 171 (02) :373-387
[2]   PERMUTATIONS ACCORDING TO EXCEEDANCE TYPE AND INVERSION NUMBER AND COMBINATORIAL INTERPRETATION OF A CONTINUED HEINE FRACTION [J].
BIANE, P .
EUROPEAN JOURNAL OF COMBINATORICS, 1993, 14 (04) :277-284
[3]   AN EXAMPLE OF A GENERALIZED BROWNIAN-MOTION [J].
BOZEJKO, M ;
SPEICHER, R .
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1991, 137 (03) :519-531
[4]   MULTICHAINS, NON-CROSSING PARTITIONS AND TREES [J].
EDELMAN, PH .
DISCRETE MATHEMATICS, 1982, 40 (2-3) :171-179
[5]   CHAIN ENUMERATION AND NON-CROSSING PARTITIONS [J].
EDELMAN, PH .
DISCRETE MATHEMATICS, 1980, 31 (02) :171-180
[6]  
FLAJOLET P, 1980, DISCRETE MATH, V32, P125, DOI 10.1016/0012-365X(80)90050-3
[7]  
Kreweras G., 1972, Discrete Math., V1, P333
[8]   R-transforms of free joint distributions and non-crossing partitions [J].
Nica, A .
JOURNAL OF FUNCTIONAL ANALYSIS, 1996, 135 (02) :271-296
[9]   ON THE STRUCTURE OF THE LATTICE OF NONCROSSING PARTITIONS [J].
SIMION, R ;
ULLMAN, D .
DISCRETE MATHEMATICS, 1991, 98 (03) :193-206
[10]   MULTIPLICATIVE FUNCTIONS ON THE LATTICE OF NON-CROSSING PARTITIONS AND FREE CONVOLUTION [J].
SPEICHER, R .
MATHEMATISCHE ANNALEN, 1994, 298 (04) :611-628