On $(2k+1, 2k+3)$-core partitions with distinct parts
  In this paper, we are mainly concerned with the enumeration of $(2k+1, 2k+3)$-core partitions with distinct parts. We derive the number and the largest size of such partitions, confirming two conjectures posed by Straub. 
Sherry H.F. Yan, Guizhi Qin, Zemin Jin, Robin D.P. Zhou
math.CO