Discrete Vector Models for Catalysis and Autocatalysis

Table 1

Incomparable, catalysable pairs of partition vectors and their corresponding catalyst partition vectors with distinguished minimal global properties of discrete vector catalysis. The significant minimal global properties are marked in bold italic letters.

	n	m	𝑛⋅𝑚	𝑑𝐮,𝐯	𝑑𝐜	𝑑𝐮,𝐯⋅𝑑𝐜	Incomparable, catalysable pair		Catalyst partition vector
							of partition vectors
							𝐮^𝑇	𝐯^𝑇	𝐜^𝑇
(a)	11	42	482	5	9	45	(4, 4, 1, 1, 1)	(5, 2, 2, 2, 0)	(10, 6, 5, 5, 4, 3, 3, 3, 3)
(b)	12	410	4 920	4	38	152	(5, 5, 1, 1)	(6, 3, 3, 0)	(36, 24, 20, 20, 16, 16, 15, 15, 12, 12, 12, 12, 10, 10, 10, 10, 9, 9, 9, 9, 8, 8, 8, 8, 8, 8, 8, 8, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6)^∗
(c)	14	3	42	4	2	8	(6, 6, 1, 1)	(8, 3, 3, 0)	(2, 1)
(d)	14	3	42	4	2	8	(6, 6, 1, 1)	(8, 3, 3, 0)	(2, 1)

∗Catalyst partition vector may not be minimal.