We exhibit a weight-preserving bijection between semi-standard Young tableaux and semi-skyline augmented fillings to provide a combinatorial proof that the Schur functions decompose into nonsymmetric functions indexed by compositions. The insertion procedure involved in the proof leads to an analogue of the Robinson-SchenstedKnuth Algorithm for semi-skyline augmented fillings. This procedure co...

Tableaux have long been used to study combinatorial properties of permutations and multiset permutations. Discovered independently by Robinson and Schensted and generalized by Knuth, the Robinson-Schensted correspondence has provided a fundamental tool for relating permutations to tableaux. In 1963, Schützenberger defined a process called evacuation on standard tableaux which gives a relationsh...

We study the combinatorics of fully commutative elements in Coxeter groups of type H n for any n > 2. Using the results, we construct certain canonical bases for non-simply-laced generalized Temperley–Lieb algebras and show how to relate them to morphisms in the category of decorated tangles.

We address the attainability of the Hashin-Shtrikman bounds for multiphase composite materials. We demonstrate that the Hashin-Shtrikman bounds are not always attainable and give new restrictions on the attainable Hashin-Shtrikman bounds in terms of the conductivities and volume fractions of the constituent phases. New optimal microstructures are also constructed to attain the Hashin-Shtrikman ...