The 52 partitions of a 5-element setThis table is a "Genji-Kô no zu" (源氏香の図), or listing of the symbols used for the 54 chapters of the Tale of Genji (early Japanese "novel"). Sometimes one of these is used as a mon, when it is called a "Genji-Kô mon" (源氏香紋).
These symbols indicate the possible groupings and subgroupings of five elements, from no element being grouped together with any other element (chapter 2) to all five elements joined in a single grouping (chapter 53), and everything in between.
In the notation used in the chapter symbols, elements which are under a common horizontal bar are grouped together -- except that where a vertical stem crosses a horizontal bar (as opposed to a corner or "T"), this does not indicate a grouping.  So the symbols for chapters 35 and 42 (shown in red in the diagram) both indicate the same grouping: elements 1, 2, and 4 in one subgroup, elements 3 and 5 in another subgroup.

The 52 possible 5-element subgroupings were expanded to 54 (the number of chapters in the Tale of Genji) by using equivalent representations for chapters 35 and 42, and by adding a special symbol for chapter 54 (shown in green in the diagram).  In the incense-distinguishing game (see en:Kōdō#Kumikō), apparently the chapter 1 symbol takes the place of the chapter 35 symbol, while the chapter 54 symbol is dropped (see File:Genjikonozu.PNG), leaving one symbol for each of the 52 possible groupings (52 is a Bell number).
Self-made graphic, generated from abstract geometry and publicly-available information. Own work
AnonMoos