Association schemes are a central notion in algebraic combinatorics. They provide a unified approach to various questions from design theory, coding theory, algebraic graph theory, discrete geometry, group theory and representation theory. This is facilitated by viewing ideas from the theory of groups and their representations from a combinatorial perspective, thus leading to a more general pic...

A New Polyhedral Approach to Combinatorial Designs. (May 2004) Ivette Arámbula Mercado, B.S., Tecnológico de Monterrey (ITESM); M.S., Tecnológico de Monterrey (ITESM) Chair of Advisory Committee: Dr. Illya V. Hicks We consider combinatorial t-design problems as discrete optimization problems. Our motivation is that only a few studies have been done on the use of exact optimization techniques in...

Combinatorial auctions allow for more expressive bidding in which participants can submit package bids with logical constraints that limit allowable outcomes. This type of auction can be useful when participants' values are complementary or when participants have production and financial constraints. However, combinatorial auctions are currently rare in practice. The main problems confronted in...

We study an adverse selection model in which a principal will allocate a set of nonidentical objects among privately informed agents. Combinatorial auctions provide an important class of examples. Agents have private information that is parametrized by a one dimensional type. The principal collects type reports from the agents, computes their valuations for di¤erent sets, and then decides on an...

Xiongfeng Ma ∗ and Xiaoqing Tan 1, † Center for Quantum Information and Quantum Control, Department of Physics and Department of Electrical & Computer Engineering, University of Toronto, Toronto, Ontario, Canada Department of Mathematics, College of Information Science and Technology, Jinan University, Guangzhou, Guangdong, P. R. China Abstract A combinatorial design is a family of sets that ar...

In the search for better performing battery materials, researchers have increasingly ventured into complex composition spaces, including numerous pseudo-quaternaries, with further substitutions being either explored experimentally or proposed based on computation. Given vast spaces that need exploring, experimental combinatorial science can play an important role in accelerating development of ...

We consider the problem of far-field sensing by means of a sensor array. Traditional array geometry design techniques are agnostic to prior information about the far-field scene. However, in many applications such priors are available and may be utilized to design more efficient array topologies. We formulate the problem of array geometry design with scene prior as one of finding a sampling con...