A Generalization of the AL method for Fair Allocation of Indivisible Objects

We consider the assignment problem in which agents express ordinal preferences over $m$ objects and the objects are allocated to the agents based on the preferences. In a recent paper, Brams, Kilgour, and Klamler (2014) presented the AL method to compute an envy-free assignment for two agents. The AL method crucially depends on the assumption that agents have strict preferences over objects. We generalize the AL method to the case where agents may express indifferences and prove the axiomatic properties satisfied by the algorithm. As a result of the generalization, we also get a $O(m)$ speedup on previous algorithms to check whether a complete envy-free assignment exists or not. Finally, we show that unless P=NP, there can be no polynomial-time extension of GAL to the case of arbitrary number of agents

Glimpse on the relationship between Feynman integral and integrable system

We briefly review recent attempts to relate the concept of Feynman integral and integrable systems. This constitutes an endeavour on our part in making the Feynman path integral into a mathematically meaningful entity