EJC
2011
12 years 8 months ago
2011
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...
APAL
1999
13 years 4 months ago
1999
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...
JCT
2000
13 years 4 months ago
2000
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 ...
COMBINATORICS
2002
13 years 4 months ago
2002
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...
COMBINATORICS
2002
13 years 4 months ago
2002
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...
SIAMCOMP
2008
13 years 5 months ago
2008
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...
JCT
2008
13 years 5 months ago
2008
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...
JCT
2008
13 years 5 months ago
2008
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...
JCT
2008
13 years 5 months ago
2008
Using classical transformations on the symmetric group and two transformations constructed in Fix-Mahonian Calculus I, we show that several multivariable statistics are equidistrib...
ARSCOM
2006
13 years 5 months ago
2006
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...