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...
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...
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 ...
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...
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...
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...
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...
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...
Using classical transformations on the symmetric group and two transformations constructed in Fix-Mahonian Calculus I, we show that several multivariable statistics are equidistrib...
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...