%0 Journal Article %T Knuth Relations for the Hyperoctahedral Groups %A Thomas Pietraho %J Mathematics %D 2008 %I arXiv %X C. Bonnaf{\'e}, M. Geck, L. Iancu, and T. Lam have conjectured a description of one-sided cells in unequal parameter Hecke algebras of type $B$ which is based on domino tableaux of arbitrary rank. In the integer case, this generalizes the work of D. Garfinkle whose methods we adapt to construct a family of operators which generate the conjectured combinatorial description. %U http://arxiv.org/abs/0803.3335v1