Special Seminar Talk: Schmidt-type theorems via weighted partition identities (Speaker: Prof. Krishnaswami Alladi, University of Florida))
Sprache des Titels:
A 1999 theorem of F. Schmidt states that the number of partitions into distinct parts whose odd-indexed parts sum to n, equals the number of partitions of n. Recently using MacMahon's partition analysis, Andrews and Paule established two further theorems of Schmidt-type. We will show that Schmidt's 1999 theorem is equivalent to a weighted partition identity involving Rogers-Ramanujan partitions that I established in 1997. Using the weighted partition approach, we provide new proofs of the two theorems of Andrews-Paule. Finally, using weighted partitions, we establish a new Schmidt type theorem which has links with two famous identities of L. J. Rogers, and with a series that Ramanujan communicated to Hardy in his last letter of 1920. NOTE. Professor Alladi is one of the leading experts on Ramanujan. For example, he is (founding) editor of the Ramanujan Journal.