Polynomiality of certain average weights for oscillating tableaux

We prove that a family of average weights for oscillating tableaux are polynomials in two variables, namely, the length of the oscillating tableau and the size of the ending partition, which generalizes a result of Hopkins and Zhang. Several explicit and asymptotic formulas for the average weights are also derived.Comment: 12 page

Difference operators for partitions under the Littlewood decomposition

The concept of $t$-difference operator for functions of partitions is introduced to prove a generalization of Stanley's theorem on polynomiality of Plancherel averages of symmetric functions related to contents and hook lengths. Our extension uses a generalization of the notion of Plancherel measure, based on walks in the Young lattice with steps given by the addition of $t$-hooks. It is well-known that the hook lengths of multiples of $t$ can be characterized by the Littlewood decomposition. Our study gives some further information on the contents and hook lengths of other congruence classes modulo $t$.Comment: 24 page

The Implementation of One Opportunistic Routing in Wireless Networks

In the paper, it proposes an optimization framework addressing fairness issues for opportunity routing in wireless mesh networks, where we use network coding to ease the routing problem. We propose a distributed heuristic algorithm in the case when scheduling is determined by MAC, and discuss the suitability of our algorithm through simulations. It is found that in most situations our algorithm has better performances than the single-path algorithm and the classical network coding which is based opportunity algorithm MORE