A Note on the Growth of Periodic Points for Commuting Toral Automorphisms

Table 3

The number of fixed points 𝑁(𝑛₁,𝑛₂) for |𝑛₁|,|𝑛₂|≤4. The columns correspond to 𝑛₁ and the rows correspond to 𝑛₂.

	−4	−3	−2	−1	0	1	2	3	4
4	13395375	1295405	61440	2645	15	125	48735	6452480	560164815
3	1613760	722000	37500	3920	540	1280	37500	524880	269340
2	141135	182405	3375	1280	15	1805	59535	2415125	79626240
1	48735	3920	15	125	15	405	19440	1245005	56745375
0	10786560	188180	960	20	∞	20	960	188180	10786560
−1	56745375	1245005	19440	405	15	125	15	3920	48735
−2	79626240	2415125	59535	1805	15	1280	3375	182405	141135
−3	269340	524880	37500	1280	540	3920	37500	722000	1613760
−4	560164815	6452480	48735	125	15	2645	61440	1295405	13395375