Chains of binary paths and shifted tableaux

Abstract

In this paper, a natural bijection between multichains of binary paths and shifted tableaux is presented, and it is used for the enumeration of the chains with maximum length from a given path $P$ to the maximum path $1_{|P|}$. By mapping chains to shifted tableaux, the main formulas given in a recent paper by the authors for the enumeration of the $P-1_{|P|}$ chains having only small intervals and minimum length are proved, using some new bijections on shifted tableaux.

17 pages

References in corpus (1)

• Chains with Small Intervals in the Lattice of Binary Paths