Discrete Vector Models for Catalysis and Autocatalysis

Table 2

Incomparable pairs of partition vectors which may be catalysable from partition lattices up to 𝑛=13 and corresponding catalyst partition vectors.

n	𝑑𝐮,𝐯	𝐮^𝑇	𝐯^𝑇	m	𝑑𝐜	𝐜^𝑇	𝑁𝐜,20
11	5	(4, 4, 1, 1, 1)	(5, 2, 2, 2, 0)	42	9	(10, 6, 5, 5, 4, 3, 3, 3, 3)	0
12	4	(5, 5, 1, 1)	(6, 3, 3, 0)	410	38	(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)^*	0
12	5	(5, 4, 1, 1, 1)	(6, 2, 2, 2, 0)	4	3	(2, 1, 1)	87
12	6	(4, 4, 1, 1, 1, 1)	(5, 2, 2, 2, 1, 0)	42	9	(10, 6, 5, 5, 4, 3, 3, 3, 3)	0
12	6	(3, 3, 3, 1, 1, 1)	(4, 2, 2, 2, 2, 0)	37	5	(12, 8, 7, 5, 5)^*	0
13	4	(6, 5, 1, 1)	(7, 3, 3, 0)	31	6	(10, 6, 5, 4, 3, 3)^*	0
13	5	(6, 4, 1, 1, 1)	(7, 2, 2, 2, 0)	4	3	(2, 1, 1)	120
13	5	(5, 5, 1, 1, 1)	(7, 2, 2, 2, 0)	4	3	(2, 1, 1)	229
13	5	(5, 5, 1, 1, 1)	(6, 3, 3, 1, 0)	410	38	(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)^*	0
13	5	(5, 5, 1, 1, 1)	(6, 3, 2, 2, 0)	?^**	?^**	?^**	?^**
13	6	(5, 4, 1, 1, 1, 1)	(6, 2, 2, 2, 1, 0)	4	3	(2, 1, 1)	87
13	6	(4, 4, 2, 1, 1, 1)	(5, 2, 2, 2, 2, 0)	42	9	(10, 6, 5, 5, 4, 3, 3, 3, 3)	0
13	7	(4, 4, 1, 1, 1, 1, 1)	(5, 2, 2, 2, 2, 0, 0)	16	4	(6, 4, 3, 3)	9
13	6	(4, 3, 3, 1, 1, 1)	(5, 2, 2, 2, 2, 0)	4	3	(2, 1, 1)	134
13	7	(4, 4, 1, 1, 1, 1, 1)	(5, 2, 2, 2, 1, 1, 0)	42	9	(10, 6, 5, 5, 4, 3, 3, 3, 3)	0
13	7	(3, 3, 3, 1, 1, 1, 1)	(4, 2, 2, 2, 2, 1, 0)	37	5	(12, 8, 7, 5, 5)^*	0

∗Catalyst partition vector may not be minimal for the respective pair.∗∗A catalyst could not yet be found by our investigations. We assume that a catalyst vector for this pair does not exist.
∗∗A catalyst could not yet be found by our investigations. We assume that a catalyst vector for this pair does not exist.