Discrete Vector Models for Catalysis and Autocatalysis

Table 3

Incomparable pairs of partition vectors u and v which exhibit Master- or Slave-Autocatalysis and are contained in partition lattices up to 𝑛=17, and incomparable pairs showing Mutual Autocatalysis of partition lattice with 𝑛=22. In addition, the type of autocatalysis and the minimal catalyst vector 𝐜_min for u and v are listed.

n	𝐮^𝑇	𝐯^𝑇	Autocatalytic partition	Type of autocatalysis	𝐜^𝑇min
15	(6, 3, 3, 1, 1, 1)	(7, 2, 2, 2, 2, 0)	u	Slave	(2, 1, 1)
16	(6, 3, 3, 1, 1, 1, 1)	(7, 2, 2, 2, 2, 1, 0)	u	Slave	(2, 1, 1)
16	(4, 4, 4, 1, 1, 1, 1)	(6, 3, 2, 2, 2, 1, 0)	v	Master	(2, 1)
16	(5, 3, 3, 1, 1, 1, 1, 1)	(6, 2, 2, 2, 2, 2, 0, 0)	u	Slave	(2, 1, 1)
17	(7, 4, 3, 1, 1, 1)	(9, 2, 2, 2, 2, 0)	u	Slave	(2, 1)
17	(6, 3, 3, 2, 1, 1, 1)	(7, 2, 2, 2, 2, 2, 0)	u	Slave	(2, 1, 1)
17	(6, 3, 3, 1, 1, 1, 1, 1)	(7, 2, 2, 2, 2, 2, 0, 0)	u	Slave	(2, 1, 1)
17	(5, 4, 3, 2, 1, 1, 1)	(7, 2, 2, 2, 2, 2, 0)	u	Slave	(2, 1)
17	(6, 3, 3, 1, 1, 1, 1, 1)	(7, 2, 2, 2, 2, 1, 1, 0)	u	Slave	(2, 1, 1)
17	(4, 4, 4, 1, 1, 1, 1, 1)	(6, 3, 2, 2, 2, 2, 0, 0)	v	Master	(2, 1)
17	(4, 4, 4, 1, 1, 1, 1, 1)	(6, 3, 2, 2, 2, 1, 1, 0)	v	Master	(2, 1)
17	(5, 3, 3, 1, 1, 1, 1, 1, 1)	(6, 2, 2, 2, 2, 2, 1, 0, 0)	u	Slave	(2, 1, 1)
22	(7, 5, 4, 3, 1, 1, 1)	(10, 4, 2, 2, 2, 2, 0)	u, v	Mutual	(2, 1)
22	(8, 5, 3, 3, 1, 1, 1)	(10, 3, 3, 2, 2, 2, 0)	u, v	Mutual	(2, 1, 1)
22	(8, 4, 4, 3, 1, 1, 1)	(10, 3, 3, 2, 2, 2, 0)	u, v	Mutual	(2, 1)
22	(6, 5, 3, 3, 1, 1, 1, 1, 1)	(9, 3, 2, 2, 2, 2, 2, 0, 0)	u, v	Mutual	(2, 1)
22	(6, 4, 4, 3, 1, 1, 1, 1, 1)	(9, 3, 2, 2, 2, 2, 2, 0, 0)	u, v	Mutual	(2, 1)
22	(6, 5, 3, 3, 1, 1, 1, 1, 1)	(9, 3, 2, 2, 2, 2, 1, 1, 0)	u, v	Mutual	(2, 1)