A272764 Number of positive roots in reflection group E_n.

3, 10, 20, 36, 63, 120

Offset: 3

Author

N. J. A. Sloane, May 05 2016

Keywords

• nonn
• fini
• full

Examples

			Starting with the Coxeter-Dynkin diagram for E_8, one repeatedly chops off nodes from one end, getting the sequence E_8, E_7, E_6, D_5, A_4, A_2 X A_1, for which the numbers of positive roots are 120, 63, 36, 20, 10, 3 X 1=3.
		

References

• J. E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge, 1990. See Table 3.2, page 80.

Links

• M. Golafshan, M. Rigo, and M. Whiteland, Computing the k-binomial complexity of generalized Thue-Morse words, arXiv:2412.18425 [math.CO], 2024. See p. 29.

Crossrefs

Cf. A272696.