Dennis EichhornAffiliation: University of California, Irvine Email: deichhor@math.uci.edu Title Of Talk: A New Decomposition of Partitions and its Arithmetic Implications. Abstract: In 1990, Garvan, Kim, and Stanton used the decomposition of a partition into its $\ell$core and $\ell$quotient to give explicit cycles of partitions which give direct concrete combinatorial proofs of the first few Ramanujan congruences for $p(n)$. Recently, Breuer, Kronholm, and the speaker discovered a new decomposition of a partition into its ``$\ell$box remainder" and ``$\ell$box quotient" which allows for the construction of new cycles which provide direct concrete combinatorial proofs of both congruences and the periodicity of $p(n,d)$, the number of partitions of $n$ into parts of size at most $d$, modulo $M$. In this talk, we discuss these decompositions, the cycles of partitions they generate, and the arithmetic implications. WARNING: This page contains MATHJAX
Last update made Mon Feb 15 11:51:21 PST 2016.
