Structure enumeration, applications and analysis

Structure enumeration is a field of study that involves the en-masse properties of discrete mathematical objects. Applications of structure enumeration are numerous in chemistry, physics, and mathematics, to name a few. Examples of the practical advances to be achieved include algorithms for testing equivalence of linear codes, used in communications, and fast enumeration of planar quartic graphs, used in knot theory. Theoretical advances will include counting of contingency tables, an important problem in statistics, and applications to a project in quantum physics. Outcomes will include advanced innovative software, extensive compilations of data, and many theoretical advances to be published in first-class journals.