A272764 Number of positive roots in reflection group E_n.

3, 10, 20, 36, 63, 120

Offset

3,1

References

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

Links

Table of n, a(n) for n=3..8.

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.

Example

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.

Crossrefs

Cf. A272696.

Sequence in context: A299692 A246520 A338631 * A293765 A295953 A005997

Adjacent sequences: A272761 A272762 A272763 * A272765 A272766 A272767

Keyword

nonn,fini,full

Author

N. J. A. Sloane, May 05 2016

Status

approved