Seminar: The Art of Bijections: Alternating Sign Matrices and Littlewood Identities
Speaker: Ilse Fischer, Professor of Mathematics, University of Vienna, Austria.
Abstract: When combinatorialists discover two families of objects that are counted by the same formula, they usually aim to prove this by constructing an explicit bijection. Such proofs often bring more clarity to a statement, may lead to interesting generalizations, and are usually aesthetically pleasing. Alternating sign matrices and plane partitions are classical objects in enumerative combinatorics that offer a variety of equinumerosity phenomena. However, for none of them there is a simple bijective proof so far, despite people have been searching for such proofs for more than 40 years already. The Littlewood identity, on the other hand, admits a bijective proof based on the famous Robinson-Schensted-Knuth correspondence, which is a fundamental algorithm underlying many bijective proofs. Recently, Littlewood-type identities related to alternating sign matrices and plane partitions have been discovered, bringing new perspectives to the previously hopeless search for bijections in this field.
Keywords:Alternating sign matrices, Littlewood identities, plane partitions,