Kazhdan-Lusztig polynomials for B3 Polynomials for Weyl group elements with a length difference less than three are always 1 and therefore not printed. P(long, long 0 1 0) = 1 P(long, long 0 1 2) = 1 P(long, long 0 1 2 0) = 1 + q P(long 0, long 0 1 2 0) = 1 + q P(long, long 0 1 2 3) = 1 P(long 0, long 0 1 2 3) = 1 P(long, long 0 1 2 0 1) = 1 + q^2 P(long 0, long 0 1 2 0 1) = 1 P(long 0 1, long 0 1 2 0 1) = 1 P(long, long 0 1 2 3 0) = 1 + q P(long 0, long 0 1 2 3 0) = 1 + q P(long 0 1, long 0 1 2 3 0) = 1 P(long, long 0 1 2 3 2) = 1 P(long 0, long 0 1 2 3 2) = 1 P(long 0 1, long 0 1 2 3 2) = 1 P(long, long 0 1 2 3 0 1) = 1 + q + q^2 P(long 0, long 0 1 2 3 0 1) = 1 + q P(long 0 1, long 0 1 2 3 0 1) = 1 + q P(long 0 1 0, long 0 1 2 3 0 1) = 1 + q P(long 0 1 2, long 0 1 2 3 0 1) = 1 P(long, long 0 1 2 3 2 0) = 1 + q P(long 0, long 0 1 2 3 2 0) = 1 + q P(long 0 1, long 0 1 2 3 2 0) = 1 P(long 0 1 0, long 0 1 2 3 2 0) = 1 P(long 0 1 2, long 0 1 2 3 2 0) = 1 P(long, long 0 1 2 3 0 1 2) = 1 + q + 2 q^2 P(long 0, long 0 1 2 3 0 1 2) = 1 + q + q^2 P(long 0 1, long 0 1 2 3 0 1 2) = 1 + q P(long 0 1 0, long 0 1 2 3 0 1 2) = 1 + q P(long 0 1 2, long 0 1 2 3 0 1 2) = 1 + q P(long 0 1 2 0, long 0 1 2 3 0 1 2) = 1 + q P(long 0 1 2 3, long 0 1 2 3 0 1 2) = 1 P(long, long 0 1 2 3 2 0 1) = 1 + 2 q + q^2 P(long 0, long 0 1 2 3 2 0 1) = 1 + 2 q P(long 0 1, long 0 1 2 3 2 0 1) = 1 + 2 q P(long 0 1 0, long 0 1 2 3 2 0 1) = 1 + q P(long 0 1 2, long 0 1 2 3 2 0 1) = 1 + q P(long 0 1 2 0, long 0 1 2 3 2 0 1) = 1 P(long 0 1 2 3, long 0 1 2 3 2 0 1) = 1 + q P(long, long 0 1 2 3 2 0 1 0) = 1 + 2 q + 2 q^2 P(long 0, long 0 1 2 3 2 0 1 0) = 1 + 2 q + 2 q^2 P(long 0 1, long 0 1 2 3 2 0 1 0) = 1 + 2 q + q^2 P(long 0 1 0, long 0 1 2 3 2 0 1 0) = 1 + 2 q + q^2 P(long 0 1 2, long 0 1 2 3 2 0 1 0) = 1 + q P(long 0 1 2 0, long 0 1 2 3 2 0 1 0) = 1 + q P(long 0 1 2 3, long 0 1 2 3 2 0 1 0) = 1 + q P(long 0 1 2 0 1, long 0 1 2 3 2 0 1 0) = 1 P(long 0 1 2 3 0, long 0 1 2 3 2 0 1 0) = 1 + q P(long 0 1 2 3 2, long 0 1 2 3 2 0 1 0) = 1 P(long, long 0 1 2 3 0 1 2 3) = 1 + q^2 + q^3 P(long 0, long 0 1 2 3 0 1 2 3) = 1 + q^3 P(long 0 1, long 0 1 2 3 0 1 2 3) = 1 P(long 0 1 0, long 0 1 2 3 0 1 2 3) = 1 P(long 0 1 2, long 0 1 2 3 0 1 2 3) = 1 P(long 0 1 2 0, long 0 1 2 3 0 1 2 3) = 1 P(long 0 1 2 3, long 0 1 2 3 0 1 2 3) = 1 P(long 0 1 2 0 1, long 0 1 2 3 0 1 2 3) = 1 P(long 0 1 2 3 0, long 0 1 2 3 0 1 2 3) = 1 P(long 0 1 2 3 2, long 0 1 2 3 0 1 2 3) = 1 P(long, long 0 1 2 3 2 0 1 2) = 1 + q + 2 q^2 + q^3 P(long 0, long 0 1 2 3 2 0 1 2) = 1 + q + q^2 P(long 0 1, long 0 1 2 3 2 0 1 2) = 1 + q + q^2 P(long 0 1 0, long 0 1 2 3 2 0 1 2) = 1 + q P(long 0 1 2, long 0 1 2 3 2 0 1 2) = 1 + q + q^2 P(long 0 1 2 0, long 0 1 2 3 2 0 1 2) = 1 + q P(long 0 1 2 3, long 0 1 2 3 2 0 1 2) = 1 P(long 0 1 2 0 1, long 0 1 2 3 2 0 1 2) = 1 + q P(long 0 1 2 3 0, long 0 1 2 3 2 0 1 2) = 1 P(long 0 1 2 3 2, long 0 1 2 3 2 0 1 2) = 1 P(long, long 0 1 2 3 2 0 1 2 0) = 1 + 2 q + 3 q^2 + 2 q^3 P(long 0, long 0 1 2 3 2 0 1 2 0) = 1 + 2 q + 3 q^2 + 2 q^3 P(long 0 1, long 0 1 2 3 2 0 1 2 0) = 1 + 2 q + 2 q^2 P(long 0 1 0, long 0 1 2 3 2 0 1 2 0) = 1 + 2 q + 2 q^2 P(long 0 1 2, long 0 1 2 3 2 0 1 2 0) = 1 + 2 q + 2 q^2 P(long 0 1 2 0, long 0 1 2 3 2 0 1 2 0) = 1 + 2 q + 2 q^2 P(long 0 1 2 3, long 0 1 2 3 2 0 1 2 0) = 1 + q P(long 0 1 2 0 1, long 0 1 2 3 2 0 1 2 0) = 1 + q P(long 0 1 2 3 0, long 0 1 2 3 2 0 1 2 0) = 1 + q P(long 0 1 2 3 2, long 0 1 2 3 2 0 1 2 0) = 1 + q P(long 0 1 2 0 1 0, long 0 1 2 3 2 0 1 2 0) = 1 + q P(long 0 1 2 3 0 1, long 0 1 2 3 2 0 1 2 0) = 1 P(long 0 1 2 3 2 1, long 0 1 2 3 2 0 1 2 0) = 1 P(long 0 1 2 3 2 0, long 0 1 2 3 2 0 1 2 0) = 1 + q P(long, long 0 1 2 3 2 0 1 2 3) = 1 + q + q^2 + 2 q^3 + q^4 P(long 0, long 0 1 2 3 2 0 1 2 3) = 1 + q + q^3 P(long 0 1, long 0 1 2 3 2 0 1 2 3) = 1 + q + q^3 P(long 0 1 0, long 0 1 2 3 2 0 1 2 3) = 1 + q P(long 0 1 2, long 0 1 2 3 2 0 1 2 3) = 1 + q P(long 0 1 2 0, long 0 1 2 3 2 0 1 2 3) = 1 + q P(long 0 1 2 3, long 0 1 2 3 2 0 1 2 3) = 1 + q P(long 0 1 2 0 1, long 0 1 2 3 2 0 1 2 3) = 1 + q P(long 0 1 2 3 0, long 0 1 2 3 2 0 1 2 3) = 1 + q P(long 0 1 2 3 2, long 0 1 2 3 2 0 1 2 3) = 1 P(long 0 1 2 3 0 1, long 0 1 2 3 2 0 1 2 3) = 1 + q P(long 0 1 2 3 2 1, long 0 1 2 3 2 0 1 2 3) = 1 P(long 0 1 2 3 2 0, long 0 1 2 3 2 0 1 2 3) = 1 P(long, long 0 1 2 3 2 0 1 2 0 1) = 1 + 2 q + 3 q^2 + 3 q^3 + q^4 P(long 0, long 0 1 2 3 2 0 1 2 0 1) = 1 + 2 q + 3 q^2 + 3 q^3 P(long 0 1, long 0 1 2 3 2 0 1 2 0 1) = 1 + 2 q + 3 q^2 + 3 q^3 P(long 0 1 0, long 0 1 2 3 2 0 1 2 0 1) = 1 + 2 q + 2 q^2 + 2 q^3 P(long 0 1 2, long 0 1 2 3 2 0 1 2 0 1) = 1 + 2 q + 2 q^2 + q^3 P(long 0 1 2 0, long 0 1 2 3 2 0 1 2 0 1) = 1 + 2 q + q^2 P(long 0 1 2 3, long 0 1 2 3 2 0 1 2 0 1) = 1 + q + q^2 P(long 0 1 2 0 1, long 0 1 2 3 2 0 1 2 0 1) = 1 + 2 q + q^2 P(long 0 1 2 3 0, long 0 1 2 3 2 0 1 2 0 1) = 1 + q P(long 0 1 2 3 2, long 0 1 2 3 2 0 1 2 0 1) = 1 + q P(long 0 1 2 0 1 0, long 0 1 2 3 2 0 1 2 0 1) = 1 + 2 q P(long 0 1 2 3 0 1, long 0 1 2 3 2 0 1 2 0 1) = 1 + q P(long 0 1 2 3 2 1, long 0 1 2 3 2 0 1 2 0 1) = 1 + q P(long 0 1 2 3 2 0, long 0 1 2 3 2 0 1 2 0 1) = 1 + q P(long 0 1 2 3 0 1 0, long 0 1 2 3 2 0 1 2 0 1) = 1 + q P(long 0 1 2 3 2 1 0, long 0 1 2 3 2 0 1 2 0 1) = 1 P(long 0 1 2 3 0 1 2, long 0 1 2 3 2 0 1 2 0 1) = 1 P(long 0 1 2 3 2 0 1, long 0 1 2 3 2 0 1 2 0 1) = 1 + q P(long, long 0 1 2 3 2 0 1 2 3 0) = 1 + 2 q + 2 q^2 + 2 q^3 + 2 q^4 P(long 0, long 0 1 2 3 2 0 1 2 3 0) = 1 + 2 q + 2 q^2 + 2 q^3 + 2 q^4 P(long 0 1, long 0 1 2 3 2 0 1 2 3 0) = 1 + 2 q + q^2 + q^3 P(long 0 1 0, long 0 1 2 3 2 0 1 2 3 0) = 1 + 2 q + q^2 + q^3 P(long 0 1 2, long 0 1 2 3 2 0 1 2 3 0) = 1 + 2 q + q^2 P(long 0 1 2 0, long 0 1 2 3 2 0 1 2 3 0) = 1 + 2 q + q^2 P(long 0 1 2 3, long 0 1 2 3 2 0 1 2 3 0) = 1 + 2 q + q^2 P(long 0 1 2 0 1, long 0 1 2 3 2 0 1 2 3 0) = 1 + q P(long 0 1 2 3 0, long 0 1 2 3 2 0 1 2 3 0) = 1 + 2 q + q^2 P(long 0 1 2 3 2, long 0 1 2 3 2 0 1 2 3 0) = 1 + q P(long 0 1 2 0 1 0, long 0 1 2 3 2 0 1 2 3 0) = 1 + q P(long 0 1 2 3 0 1, long 0 1 2 3 2 0 1 2 3 0) = 1 + q P(long 0 1 2 3 2 1, long 0 1 2 3 2 0 1 2 3 0) = 1 P(long 0 1 2 3 2 0, long 0 1 2 3 2 0 1 2 3 0) = 1 + q P(long 0 1 2 3 0 1 0, long 0 1 2 3 2 0 1 2 3 0) = 1 + q P(long 0 1 2 3 2 1 0, long 0 1 2 3 2 0 1 2 3 0) = 1 P(long 0 1 2 3 0 1 2, long 0 1 2 3 2 0 1 2 3 0) = 1 P(long 0 1 2 3 2 0 1, long 0 1 2 3 2 0 1 2 3 0) = 1 P(long, long 0 1 2 3 2 0 1 2 3 0 1) = 1 + 2 q + 2 q^2 + 2 q^3 + q^4 + q^5 P(long 0, long 0 1 2 3 2 0 1 2 3 0 1) = 1 + 2 q + 2 q^2 + 2 q^3 + q^4 P(long 0 1, long 0 1 2 3 2 0 1 2 3 0 1) = 1 + 2 q + 2 q^2 + 2 q^3 + q^4 P(long 0 1 0, long 0 1 2 3 2 0 1 2 3 0 1) = 1 + 2 q + q^2 + q^3 P(long 0 1 2, long 0 1 2 3 2 0 1 2 3 0 1) = 1 + 2 q + q^2 + q^3 P(long 0 1 2 0, long 0 1 2 3 2 0 1 2 3 0 1) = 1 + 2 q P(long 0 1 2 3, long 0 1 2 3 2 0 1 2 3 0 1) = 1 + 2 q + q^2 + q^3 P(long 0 1 2 0 1, long 0 1 2 3 2 0 1 2 3 0 1) = 1 + 2 q P(long 0 1 2 3 0, long 0 1 2 3 2 0 1 2 3 0 1) = 1 + 2 q P(long 0 1 2 3 2, long 0 1 2 3 2 0 1 2 3 0 1) = 1 + q P(long 0 1 2 0 1 0, long 0 1 2 3 2 0 1 2 3 0 1) = 1 + 2 q P(long 0 1 2 3 0 1, long 0 1 2 3 2 0 1 2 3 0 1) = 1 + 2 q P(long 0 1 2 3 2 1, long 0 1 2 3 2 0 1 2 3 0 1) = 1 + q P(long 0 1 2 3 2 0, long 0 1 2 3 2 0 1 2 3 0 1) = 1 + q P(long 0 1 2 3 0 1 0, long 0 1 2 3 2 0 1 2 3 0 1) = 1 + 2 q P(long 0 1 2 3 2 1 0, long 0 1 2 3 2 0 1 2 3 0 1) = 1 P(long 0 1 2 3 0 1 2, long 0 1 2 3 2 0 1 2 3 0 1) = 1 P(long 0 1 2 3 2 0 1, long 0 1 2 3 2 0 1 2 3 0 1) = 1 + q P(long 0 1 2 3 2 1 0 1, long 0 1 2 3 2 0 1 2 3 0 1) = 1 P(long 0 1 2 3 0 1 2 0, long 0 1 2 3 2 0 1 2 3 0 1) = 1 P(long 0 1 2 3 2 0 1 0, long 0 1 2 3 2 0 1 2 3 0 1) = 1 P(long 0 1 2 3 0 1 2 3, long 0 1 2 3 2 0 1 2 3 0 1) = 1 P(long 0 1 2 3 2 0 1 2, long 0 1 2 3 2 0 1 2 3 0 1) = 1 P(long, long 0 1 2 3 2 0 1 2 3 0 1 2) = 1 + 3 q + 4 q^2 + 4 q^3 + 3 q^4 + 2 q^5 P(long 0, long 0 1 2 3 2 0 1 2 3 0 1 2) = 1 + 3 q + 4 q^2 + 4 q^3 + 3 q^4 + q^5 P(long 0 1, long 0 1 2 3 2 0 1 2 3 0 1 2) = 1 + 3 q + 4 q^2 + 3 q^3 + 2 q^4 P(long 0 1 0, long 0 1 2 3 2 0 1 2 3 0 1 2) = 1 + 3 q + 3 q^2 + q^3 P(long 0 1 2, long 0 1 2 3 2 0 1 2 3 0 1 2) = 1 + 3 q + 4 q^2 + 3 q^3 + 2 q^4 P(long 0 1 2 0, long 0 1 2 3 2 0 1 2 3 0 1 2) = 1 + 3 q + 3 q^2 + q^3 P(long 0 1 2 3, long 0 1 2 3 2 0 1 2 3 0 1 2) = 1 + 3 q + 2 q^2 + q^3 P(long 0 1 2 0 1, long 0 1 2 3 2 0 1 2 3 0 1 2) = 1 + 3 q + 2 q^2 P(long 0 1 2 3 0, long 0 1 2 3 2 0 1 2 3 0 1 2) = 1 + 3 q + q^2 P(long 0 1 2 3 2, long 0 1 2 3 2 0 1 2 3 0 1 2) = 1 + 3 q + 2 q^2 + q^3 P(long 0 1 2 0 1 0, long 0 1 2 3 2 0 1 2 3 0 1 2) = 1 + 3 q + 2 q^2 P(long 0 1 2 3 0 1, long 0 1 2 3 2 0 1 2 3 0 1 2) = 1 + 3 q P(long 0 1 2 3 2 1, long 0 1 2 3 2 0 1 2 3 0 1 2) = 1 + 2 q + q^2 P(long 0 1 2 3 2 0, long 0 1 2 3 2 0 1 2 3 0 1 2) = 1 + 3 q + q^2 P(long 0 1 2 3 0 1 0, long 0 1 2 3 2 0 1 2 3 0 1 2) = 1 + 3 q P(long 0 1 2 3 2 1 0, long 0 1 2 3 2 0 1 2 3 0 1 2) = 1 + q P(long 0 1 2 3 0 1 2, long 0 1 2 3 2 0 1 2 3 0 1 2) = 1 + 3 q P(long 0 1 2 3 2 0 1, long 0 1 2 3 2 0 1 2 3 0 1 2) = 1 + 2 q P(long 0 1 2 3 2 1 0 1, long 0 1 2 3 2 0 1 2 3 0 1 2) = 1 P(long 0 1 2 3 0 1 2 0, long 0 1 2 3 2 0 1 2 3 0 1 2) = 1 + 3 q P(long 0 1 2 3 2 0 1 0, long 0 1 2 3 2 0 1 2 3 0 1 2) = 1 + q P(long 0 1 2 3 0 1 2 3, long 0 1 2 3 2 0 1 2 3 0 1 2) = 1 + q P(long 0 1 2 3 2 0 1 2, long 0 1 2 3 2 0 1 2 3 0 1 2) = 1 + 2 q P(long 0 1 2 3 2 1 0 1 2, long 0 1 2 3 2 0 1 2 3 0 1 2) = 1 P(long 0 1 2 3 0 1 2 0 1, long 0 1 2 3 2 0 1 2 3 0 1 2) = 1 + q P(long 0 1 2 3 2 1 0 1 0, long 0 1 2 3 2 0 1 2 3 0 1 2) = 1 P(long 0 1 2 3 0 1 2 3 0, long 0 1 2 3 2 0 1 2 3 0 1 2) = 1 + q P(long 0 1 2 3 2 0 1 2 0, long 0 1 2 3 2 0 1 2 3 0 1 2) = 1 + q P(long 0 1 2 3 2 0 1 2 3, long 0 1 2 3 2 0 1 2 3 0 1 2) = 1 P(long, long 0 1 2 3 2 0 1 2 3 0 1 2 3) = 1 + 2 q + 3 q^2 + 4 q^3 + 3 q^4 + 2 q^5 P(long 0, long 0 1 2 3 2 0 1 2 3 0 1 2 3) = 1 + 2 q + 3 q^2 + 4 q^3 + 3 q^4 + q^5 P(long 0 1, long 0 1 2 3 2 0 1 2 3 0 1 2 3) = 1 + 2 q + 3 q^2 + 4 q^3 + 2 q^4 + q^5 P(long 0 1 0, long 0 1 2 3 2 0 1 2 3 0 1 2 3) = 1 + 2 q + 2 q^2 + 2 q^3 P(long 0 1 2, long 0 1 2 3 2 0 1 2 3 0 1 2 3) = 1 + 2 q + 3 q^2 + 3 q^3 + q^4 P(long 0 1 2 0, long 0 1 2 3 2 0 1 2 3 0 1 2 3) = 1 + 2 q + 2 q^2 + q^3 P(long 0 1 2 3, long 0 1 2 3 2 0 1 2 3 0 1 2 3) = 1 + 2 q + 3 q^2 + 3 q^3 + q^4 P(long 0 1 2 0 1, long 0 1 2 3 2 0 1 2 3 0 1 2 3) = 1 + 2 q + 2 q^2 P(long 0 1 2 3 0, long 0 1 2 3 2 0 1 2 3 0 1 2 3) = 1 + 2 q + 2 q^2 + q^3 P(long 0 1 2 3 2, long 0 1 2 3 2 0 1 2 3 0 1 2 3) = 1 + 2 q + 2 q^2 + 2 q^3 P(long 0 1 2 0 1 0, long 0 1 2 3 2 0 1 2 3 0 1 2 3) = 1 + 2 q + 2 q^2 P(long 0 1 2 3 0 1, long 0 1 2 3 2 0 1 2 3 0 1 2 3) = 1 + 2 q + 2 q^2 P(long 0 1 2 3 2 1, long 0 1 2 3 2 0 1 2 3 0 1 2 3) = 1 + q + 2 q^2 + q^3 P(long 0 1 2 3 2 0, long 0 1 2 3 2 0 1 2 3 0 1 2 3) = 1 + 2 q + q^2 P(long 0 1 2 3 0 1 0, long 0 1 2 3 2 0 1 2 3 0 1 2 3) = 1 + 2 q + 2 q^2 P(long 0 1 2 3 2 1 0, long 0 1 2 3 2 0 1 2 3 0 1 2 3) = 1 + q^2 P(long 0 1 2 3 0 1 2, long 0 1 2 3 2 0 1 2 3 0 1 2 3) = 1 + 2 q P(long 0 1 2 3 2 0 1, long 0 1 2 3 2 0 1 2 3 0 1 2 3) = 1 + q + q^2 P(long 0 1 2 3 2 1 0 1, long 0 1 2 3 2 0 1 2 3 0 1 2 3) = 1 P(long 0 1 2 3 0 1 2 0, long 0 1 2 3 2 0 1 2 3 0 1 2 3) = 1 + 2 q P(long 0 1 2 3 2 0 1 0, long 0 1 2 3 2 0 1 2 3 0 1 2 3) = 1 + q^2 P(long 0 1 2 3 0 1 2 3, long 0 1 2 3 2 0 1 2 3 0 1 2 3) = 1 + 2 q P(long 0 1 2 3 2 0 1 2, long 0 1 2 3 2 0 1 2 3 0 1 2 3) = 1 + q P(long 0 1 2 3 2 1 0 1 2, long 0 1 2 3 2 0 1 2 3 0 1 2 3) = 1 P(long 0 1 2 3 0 1 2 0 1, long 0 1 2 3 2 0 1 2 3 0 1 2 3) = 1 + q P(long 0 1 2 3 2 1 0 1 0, long 0 1 2 3 2 0 1 2 3 0 1 2 3) = 1 P(long 0 1 2 3 0 1 2 3 0, long 0 1 2 3 2 0 1 2 3 0 1 2 3) = 1 + 2 q P(long 0 1 2 3 2 0 1 2 0, long 0 1 2 3 2 0 1 2 3 0 1 2 3) = 1 P(long 0 1 2 3 2 0 1 2 3, long 0 1 2 3 2 0 1 2 3 0 1 2 3) = 1 + q P(long 0 1 2 3 2 1 0 1 2 3, long 0 1 2 3 2 0 1 2 3 0 1 2 3) = 1 P(long 0 1 2 3 2 1 0 1 2 0, long 0 1 2 3 2 0 1 2 3 0 1 2 3) = 1 P(long 0 1 2 3 2 0 1 2 3 2, long 0 1 2 3 2 0 1 2 3 0 1 2 3) = 1 P(long 0 1 2 3 0 1 2 3 0 1, long 0 1 2 3 2 0 1 2 3 0 1 2 3) = 1 + q P(long 0 1 2 3 2 0 1 2 0 1, long 0 1 2 3 2 0 1 2 3 0 1 2 3) = 1 P(long 0 1 2 3 2 0 1 2 3 0, long 0 1 2 3 2 0 1 2 3 0 1 2 3) = 1