Armin StraubAffiliation: University of South Alabama Email: straub@southalabama.edu Title Of Talk: Core partitions into distinct parts and an analog of Euler's theorem Abstract: A special case of an elegant result due to Anderson proves that the number of $(s,s+1)$core partitions is finite and is given by the Catalan number $C_s$. Amdeberhan recently conjectured that the number of $(s,s+1)$core partitions into distinct parts equals the Fibonacci number $F_{s+1}$. We prove this conjecture by enumerating, more generally, $(s,ds1)$core partitions into distinct parts. As a byproduct of our discussion, we obtain a bijection between partitions into distinct parts and partitions into odd parts, which preserves the perimeter (that is, the largest part plus the number of parts minus $1$). This simple but curious analog of Euler's theorem appears to be missing from the literature on partitions. WARNING: This page contains MATHJAX
Last update made Thu Jan 21 17:43:26 PST 2016.
