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EJC
2011
13 years 3 months ago
Two enumerative results on cycles of permutations
Answering a question of B´ona, it is shown that for n ≥ 2 the probability that 1 and 2 are in the same cycle of a product of two n-cycles on the set {1, 2, . . . , n} is 1/2 if...
Richard P. Stanley
APAL
1999
90views more  APAL 1999»
13 years 11 months ago
On Distinguishing Quotients of Symmetric Groups
A study is carried out of the elementary theory of quotients of symmetric groups in a similar spirit to [10]. Apart from the trivial and alternating subgroups, the normal subgroup...
Saharon Shelah, J. K. Truss
JCT
2000
111views more  JCT 2000»
13 years 11 months ago
Immanants and Finite Point Processes
Givena Hermitian,non-negativede nitekernelK and a character of the symmetric group on n letters, de ne the corresponding immanant function K x1;::: ;xn := P Qn i=1 Kxi;x i, where ...
Persi Diaconis, Steven N. Evans
COMBINATORICS
2002
107views more  COMBINATORICS 2002»
13 years 11 months ago
Combinatorial Laplacian of the Matching Complex
A striking result of Bouc gives the decomposition of the representation of the symmetric group on the homology of the matching complex into irreducibles that are self-conjugate. We...
Xun Dong, Michelle L. Wachs
COMBINATORICS
2002
85views more  COMBINATORICS 2002»
13 years 11 months ago
Parking Functions of Types A and B
The lattice of noncrossing partitions can be embedded into the Cayley graph of the symmetric group. This allows us to rederive connections between noncrossing partitions and parki...
Philippe Biane
SIAMCOMP
2008
80views more  SIAMCOMP 2008»
13 years 11 months ago
The Symmetric Group Defies Strong Fourier Sampling
Part I of this paper showed that the hidden subgroup problem over the symmetric group--including the special case relevant to Graph Isomorphism--cannot be efficiently solved by st...
Cristopher Moore, Alexander Russell, Leonard J. Sc...
JCT
2008
132views more  JCT 2008»
13 years 11 months ago
The absolute order on the symmetric group, constructible partially ordered sets and Cohen-Macaulay complexes
The absolute order is a natural partial order on a Coxeter group W. It can be viewed as an analogue of the weak order on W in which the role of the generating set of simple reflec...
Christos A. Athanasiadis, Myrto Kallipoliti
JCT
2008
103views more  JCT 2008»
13 years 11 months ago
A bijective proof of Jackson's formula for the number of factorizations of a cycle
Factorizations of the cyclic permutation (1 2 . . . N) into two permutations with respectively n and m cycles, or, equivalently, unicellular bicolored maps with N edges and n whit...
Gilles Schaeffer, Ekaterina A. Vassilieva
JCT
2008
84views more  JCT 2008»
13 years 11 months ago
Fix-Mahonian Calculus, II: Further statistics
Using classical transformations on the symmetric group and two transformations constructed in Fix-Mahonian Calculus I, we show that several multivariable statistics are equidistrib...
Dominique Foata, Guo-Niu Han
ARSCOM
2006
91views more  ARSCOM 2006»
13 years 11 months ago
Binary codes from graphs on triples and permutation decoding
We show that permutation decoding can be used, and give explicit PD-sets in the symmetric group, for some of the binary codes obtained from the adjacency matrices of the graphs on...
Jennifer D. Key, Jamshid Moori, Bernardo Gabriel R...