Counting monogenic monoids and inverse monoids

Figures & data

Table 1. The values of the functions $(n)\mathbf{s}$, $(n)\mathbf{t}$, and $(n)\mathbf{i}$ for some small values of n.

n	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19
$(n)\mathbf{s}$	1	1	2	3	4	6	6	9	11	14	16	20	23	27	31	35	43	47	55	61
$(n)\mathbf{t}$	1	1	3	6	10	16	22	31	42	56	72	92	115	142	173	208	251	298	353	414
$(n)\mathbf{i}$	1	2	4	7	11	17	23	32	43	57	73	93	116	143	174	209	252	299	354	415

Figure 1. Functional digraph of a transformation on 11 points with threshold 2 and period 3.

Figure 2. Munn tree for the free inverse monoid element $\mathit{aba}{a}^{-1}baa{a}^{-1}{a}^{-1}b$ with start $\alpha$ and end $\omega$.