A Framework for Coxeter Spectral Classification of Finite Posets and Their Mesh Geometries of Roots

Table 2

𝑗	𝑢^(𝑗)	𝑢+^(𝑗)	𝑤^(𝑗)	𝑤+^(𝑗)	𝑣^(𝑗)	𝑣+^(𝑗)
𝑗=0	−𝑒5=(0,0,0,0,−1)	(1,1,−1,−1,1)	(1,0,0,−1,0)	(0,1,−1,0,0)	(0,1,0,−1,0)	(1,0,−1,0,0,)
𝑗=1	(2,2,−2,−2,1)	(1,1,−1,−1,−1)	(1,2,−2,−1,0)	(2,1,−1,−2,0)	(2,1,−2,−1,0)	(1,2,−1,−2,0)
𝑗=2	(2,2,−2,−2,−1)	(3,3,−3,−3,1)	(3,2,−2,−3,0)	(2,3,−3,−2,0)	(2,3,−2,−3,0)	(3,2,−3,−2,0)
𝑗=3	(4,4,−4,−4,1)	(3,3,−3,−3,−1)	(3,4,−4,−3,0)	(4,3,−3,−4,0)	(4,3,−4,−3,0)	(3,4,−3,−4,0)
𝑗=4	(4,4,−4,−4,−1)	(5,5,−5,−5,1)	(5,4,−4,−5,0)	(4,5,−5,−4,0)	(4,5,−4,−5,0)	(5,4,−5,−4,0)
𝑗=5	(6,6,−6,−6,1)	(5,5,−5,−5,−1)	(5,6,−6,−5,0)	(6,5,−5,−6,0)	(6,5,−6,−5,0)	(5,6,−5,−6,0)
𝑗=6	(6,6,−6,−6,−1)	(7,7,−7,−7,1)	(7,6,−6,−7,0)	(6,7,−7,−6,0)	(6,7,−6,−7,0)	(7,6,−7,−6,0)
𝑗=7	(8,8,−8,−8,1)	(7,7,−7,−7,−1)	(7,8,−8,−7,0)	(8,7,−7,−8,0)	(8,7,−8,−7,0)	(7,8,−7,−8,0)
⋮	⋮	⋮	⋮	⋮	⋮	⋮