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A central theme in combinatorics is to count how many objects there are in a certain structure. Extending this, one seeks to produce a bijective correspondence between two given structures. Accomplishing this may bring in various algebraic techniques, involving symmetries for example, though beyond any general collection of algebraic techniques, combinatorics has its own domain. Members of our department do research in combinatorial aspects of representations of Lie groups, entities for enumeration, characters, and special functions, matroid theory, and finite geometries.