Exhaustive expansion: A novel technique for analyzing complex data generated by higher-order polychromatic flow cytometry experiments

Table 2 Combinations of positive/negative phenotypes in a 5-marker panel.

Number of markers (M)	Number of +/- gates given M markers (G)	Combinations	Number of combinations of M markers in a 5 marker panel (C)	Number of gates times number of combinations (G × C)
0	2⁰ = 1	No markers specified	1	1
1	2¹ = 2	A, B, C, D, E	5	10
2	2² = 4	AB, AC, AD, AE, BC, BD, BE, CD, CE, DE	10	40
3	2³ = 8	ABC, ABD, ABE, ACD, ACE, ADE, BCD, BCE, BDE, CDE	10	80
4	2⁴ = 16	ABCD, ABCE, ABDE, ACDE, BCDE	5	80
5	2⁵ = 32	ABCDE	1	32
				TOTAL = 243

This table illustrates the total number of positive/negative gates in a 5-marker panel, with hypothetical markers A, B, C, D and E. There are five possible 1-marker combinations, ten 2-marker combinations, ten 3-marker combinations, five 4-marker combinations, and one 5-marker combination. For each combination, there are 2^M positive/negative gates where M is the number of markers in the combinations. Thus, there are 243 possible phenotypes in a 5 marker experiment. This generalizes to 3^M.

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