Algorithmic Combinatorics Seminar and Computer Algebra Seminar

Title: Schmidt-type theorems via weighted partition identities

Speaker: Prof. Dr. Krishnaswami Alladi
         (University of Florida, U.S.A.)

Time and Location: Wednesday, September 28, 2022, 2 p.m
                   RISC castle seminar room

Abstract: 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.