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SSM-Tp’s, l=4

SSM-Thom polynomials up to cohomological degree 24

of

contact singularities of relative dimension l=4 up to codimension 12

the singularities

codimension 0

Local algebra C
Thom-Boardman class \Sigma^0
Codimension 0
SSM-Thom polynomial in Chern classes 1 -T^5c_{5} +T^6(c_{1}c_{5} +4c_{6}) +T^7( -c_{1}^2c_{5} -5c_{1}c_{6} +c_{2}c_{5} -10c_{7}) +T^8(c_{1}^3c_{5} +6c_{1}^2c_{6} -2c_{1}c_{2}c_{5} +15c_{1}c_{7} -6c_{2}c_{6} +c_{3}c_{5} +20c_{8}) +T^9( -c_{1}^4c_{5} -7c_{1}^3c_{6} +3c_{1}^2c_{2}c_{5} -21c_{1}^2c_{7} +14c_{1}c_{2}c_{6} -2c_{1}c_{3}c_{5} -c_{2}^2c_{5} -35c_{1}c_{8} +21c_{2}c_{7} -7c_{3}c_{6} +c_{4}c_{5} -35c_{9}) +T^10(c_{1}^5c_{5} +8c_{1}^4c_{6} -4c_{1}^3c_{2}c_{5} +28c_{1}^3c_{7} -24c_{1}^2c_{2}c_{6} +3c_{1}^2c_{3}c_{5} +3c_{1}c_{2}^2c_{5} +56c_{1}^2c_{8} -56c_{1}c_{2}c_{7} +16c_{1}c_{3}c_{6} -2c_{1}c_{4}c_{5} +8c_{2}^2c_{6} -2c_{2}c_{3}c_{5} +70c_{1}c_{9} -56c_{2}c_{8} +28c_{3}c_{7} -8c_{4}c_{6} +c_{5}^2 +56c_{10}) +T^11( -c_{1}^6c_{5} -9c_{1}^5c_{6} +5c_{1}^4c_{2}c_{5} -36c_{1}^4c_{7} +36c_{1}^3c_{2}c_{6} -4c_{1}^3c_{3}c_{5} -6c_{1}^2c_{2}^2c_{5} -84c_{1}^3c_{8} +108c_{1}^2c_{2}c_{7} -27c_{1}^2c_{3}c_{6} +3c_{1}^2c_{4}c_{5} -27c_{1}c_{2}^2c_{6} +6c_{1}c_{2}c_{3}c_{5} +c_{2}^3c_{5} -126c_{1}^2c_{9} +168c_{1}c_{2}c_{8} -72c_{1}c_{3}c_{7} +18c_{1}c_{4}c_{6} -2c_{1}c_{5}^2 -36c_{2}^2c_{7} +18c_{2}c_{3}c_{6} -2c_{2}c_{4}c_{5} -c_{3}^2c_{5} -126c_{1}c_{10} +126c_{2}c_{9} -84c_{3}c_{8} +36c_{4}c_{7} -8c_{5}c_{6} -84c_{11}) +T^12(c_{1}^7c_{5} +10c_{1}^6c_{6} -6c_{1}^5c_{2}c_{5} +45c_{1}^5c_{7} -50c_{1}^4c_{2}c_{6} +5c_{1}^4c_{3}c_{5} +10c_{1}^3c_{2}^2c_{5} +120c_{1}^4c_{8} -180c_{1}^3c_{2}c_{7} +40c_{1}^3c_{3}c_{6} -4c_{1}^3c_{4}c_{5} +60c_{1}^2c_{2}^2c_{6} -12c_{1}^2c_{2}c_{3}c_{5} -4c_{1}c_{2}^3c_{5} +210c_{1}^3c_{9} -360c_{1}^2c_{2}c_{8} +135c_{1}^2c_{3}c_{7} -30c_{1}^2c_{4}c_{6} +3c_{1}^2c_{5}^2 +135c_{1}c_{2}^2c_{7} -60c_{1}c_{2}c_{3}c_{6} +6c_{1}c_{2}c_{4}c_{5} +3c_{1}c_{3}^2c_{5} -10c_{2}^3c_{6} +3c_{2}^2c_{3}c_{5} +252c_{1}^2c_{10} -420c_{1}c_{2}c_{9} +240c_{1}c_{3}c_{8} -90c_{1}c_{4}c_{7} +18c_{1}c_{5}c_{6} +120c_{2}^2c_{8} -90c_{2}c_{3}c_{7} +20c_{2}c_{4}c_{6} -2c_{2}c_{5}^2 +10c_{3}^2c_{6} -2c_{3}c_{4}c_{5} +210c_{1}c_{11} -252c_{2}c_{10} +210c_{3}c_{9} -120c_{4}c_{8} +45c_{5}c_{7} -9c_{6}^2 +120c_{12})
SSM-Thom polynomial in Schur functions -T^5s_{5} +s_{0} +T^6(5s_{6} +s_{5,1}) +T^7( -15s_{7} -6s_{6,1} -s_{5,1,1}) +T^8(s_{5,1,1,1} +7s_{6,1,1} +21s_{7,1} +35s_{8}) +T^9( -s_{5,1,1,1,1} -8s_{6,1,1,1} -28s_{7,1,1} -56s_{8,1} -70s_{9}) +T^10(s_{5,1,1,1,1,1} +9s_{6,1,1,1,1} +36s_{7,1,1,1} +84s_{8,1,1} +126s_{9,1} +126s_{10}) +T^11( -s_{5,1,1,1,1,1,1} -10s_{6,1,1,1,1,1} -45s_{7,1,1,1,1} -120s_{8,1,1,1} -210s_{9,1,1} -252s_{10,1} -210s_{11}) +T^12(330s_{9,1,1,1} +462s_{10,1,1} +462s_{11,1} +330s_{12} +s_{5,1,1,1,1,1,1,1} +11s_{6,1,1,1,1,1,1} +s_{6,6} +55s_{7,1,1,1,1,1} +165s_{8,1,1,1,1})
SSM-Thom polynomial in Schur-tilde functions (S_{2,2,2,2,2,2} +S_{4,1,1,1,1,1,1,1,1} +S_{4,2,1,1,1,1,1,1} +S_{4,2,2,1,1,1,1} +S_{1,1,1,1,1,1,1,1,1,1,1,1} +S_{2,1,1,1,1,1,1,1,1,1,1} +S_{3,1,1,1,1,1,1,1,1,1} +S_{3,2,1,1,1,1,1,1,1} +S_{4,2,2,2,1,1} +S_{4,2,2,2,2} +S_{4,3,1,1,1,1,1} +S_{4,3,2,1,1,1} +S_{4,3,2,2,1} +S_{4,3,3,1,1} +S_{4,3,3,2} +S_{4,4,1,1,1,1} +S_{4,4,2,1,1} +S_{4,4,2,2} +S_{4,4,3,1} +S_{4,4,4} +S_{2,2,1,1,1,1,1,1,1,1} +S_{2,2,2,1,1,1,1,1,1} +S_{2,2,2,2,1,1,1,1} +S_{2,2,2,2,2,1,1} +S_{3,2,2,1,1,1,1,1} +S_{3,2,2,2,1,1,1} +S_{3,2,2,2,2,1} +S_{3,3,1,1,1,1,1,1} +S_{3,3,2,1,1,1,1} +S_{3,3,2,2,1,1} +S_{3,3,2,2,2} +S_{3,3,3,1,1,1} +S_{3,3,3,2,1} +S_{3,3,3,3})T^12 +(S_{4,3,2,2} +S_{4,3,3,1} +S_{4,4,1,1,1} +S_{4,4,2,1} +S_{4,4,3} +S_{2,2,1,1,1,1,1,1,1} +S_{2,2,2,1,1,1,1,1} +S_{2,2,2,2,1,1,1} +S_{2,2,2,2,2,1} +S_{3,2,2,1,1,1,1} +S_{3,2,2,2,1,1} +S_{3,2,2,2,2} +S_{3,3,1,1,1,1,1} +S_{3,3,2,1,1,1} +S_{3,3,2,2,1} +S_{3,3,3,1,1} +S_{3,3,3,2} +S_{4,2,2,2,1} +S_{4,3,1,1,1,1} +S_{4,3,2,1,1} +S_{4,2,2,1,1,1} +S_{1,1,1,1,1,1,1,1,1,1,1} +S_{2,1,1,1,1,1,1,1,1,1} +S_{3,1,1,1,1,1,1,1,1} +S_{3,2,1,1,1,1,1,1} +S_{4,1,1,1,1,1,1,1} +S_{4,2,1,1,1,1,1})T^11 +(S_{1,1,1,1,1,1,1,1,1,1} +S_{2,1,1,1,1,1,1,1,1} +S_{2,2,1,1,1,1,1,1} +S_{2,2,2,1,1,1,1} +S_{2,2,2,2,1,1} +S_{2,2,2,2,2} +S_{3,1,1,1,1,1,1,1} +S_{3,2,1,1,1,1,1} +S_{3,2,2,1,1,1} +S_{3,2,2,2,1} +S_{3,3,1,1,1,1} +S_{3,3,2,1,1} +S_{3,3,2,2} +S_{3,3,3,1} +S_{4,1,1,1,1,1,1} +S_{4,2,1,1,1,1} +S_{4,2,2,1,1} +S_{4,2,2,2} +S_{4,3,1,1,1} +S_{4,3,2,1} +S_{4,3,3} +S_{4,4,1,1} +S_{4,4,2})T^10 +(S_{1,1,1,1,1,1,1,1,1} +S_{2,1,1,1,1,1,1,1} +S_{2,2,1,1,1,1,1} +S_{2,2,2,1,1,1} +S_{2,2,2,2,1} +S_{3,1,1,1,1,1,1} +S_{3,2,1,1,1,1} +S_{3,2,2,1,1} +S_{3,2,2,2} +S_{3,3,1,1,1} +S_{3,3,2,1} +S_{3,3,3} +S_{4,1,1,1,1,1} +S_{4,2,1,1,1} +S_{4,2,2,1} +S_{4,3,1,1} +S_{4,3,2} +S_{4,4,1})T^9 +(S_{4,4} +S_{1,1,1,1,1,1,1,1} +S_{2,1,1,1,1,1,1} +S_{2,2,1,1,1,1} +S_{2,2,2,1,1} +S_{2,2,2,2} +S_{3,1,1,1,1,1} +S_{3,2,1,1,1} +S_{3,2,2,1} +S_{3,3,1,1} +S_{3,3,2} +S_{4,1,1,1,1} +S_{4,2,1,1} +S_{4,2,2} +S_{4,3,1})T^8 +(S_{1,1,1,1,1,1,1} +S_{2,1,1,1,1,1} +S_{2,2,1,1,1} +S_{2,2,2,1} +S_{3,1,1,1,1} +S_{3,2,1,1} +S_{3,2,2} +S_{3,3,1} +S_{4,1,1,1} +S_{4,2,1} +S_{4,3})T^7 +(S_{1,1,1,1,1,1} +S_{2,1,1,1,1} +S_{2,2,1,1} +S_{2,2,2} +S_{3,1,1,1} +S_{3,2,1} +S_{4,1,1} +S_{4,2} +S_{3,3})T^6 +(S_{1,1,1,1,1} +S_{2,1,1,1} +S_{2,2,1} +S_{3,1,1} +S_{3,2} +S_{4,1})T^5 +(S_{1,1,1,1} +S_{2,1,1} +S_{3,1} +S_{2,2} +S_{4})T^4 +(S_{1,1,1} +S_{2,1} +S_{3})T^3 +(S_{2} +S_{1,1})T^2 +TS_{1} +S_{}

codimension 5

Local algebra C[x]/(x^2)
Thom-Boardman class \Sigma^{1,0}
Codimension 5
SSM-Thom polynomial in Chern classes T^5c_{5} +T^6( -c_{1}c_{5} -4c_{6}) +T^7(c_{1}^2c_{5} +5c_{1}c_{6} -c_{2}c_{5} +10c_{7}) +T^8( -c_{1}^3c_{5} -6c_{1}^2c_{6} +2c_{1}c_{2}c_{5} -15c_{1}c_{7} +6c_{2}c_{6} -c_{3}c_{5} -20c_{8}) +T^9(c_{1}^4c_{5} +7c_{1}^3c_{6} -3c_{1}^2c_{2}c_{5} +21c_{1}^2c_{7} -14c_{1}c_{2}c_{6} +2c_{1}c_{3}c_{5} +c_{2}^2c_{5} +35c_{1}c_{8} -21c_{2}c_{7} +7c_{3}c_{6} -c_{4}c_{5} +35c_{9}) +T^10( -c_{1}^5c_{5} -8c_{1}^4c_{6} +4c_{1}^3c_{2}c_{5} -28c_{1}^3c_{7} +24c_{1}^2c_{2}c_{6} -3c_{1}^2c_{3}c_{5} -3c_{1}c_{2}^2c_{5} -56c_{1}^2c_{8} +56c_{1}c_{2}c_{7} -16c_{1}c_{3}c_{6} +2c_{1}c_{4}c_{5} -8c_{2}^2c_{6} +2c_{2}c_{3}c_{5} -78c_{1}c_{9} +52c_{2}c_{8} -30c_{3}c_{7} +7c_{4}c_{6} -2c_{5}^2 -72c_{10}) +T^11(c_{1}^6c_{5} +9c_{1}^5c_{6} -5c_{1}^4c_{2}c_{5} +36c_{1}^4c_{7} -36c_{1}^3c_{2}c_{6} +4c_{1}^3c_{3}c_{5} +6c_{1}^2c_{2}^2c_{5} +84c_{1}^3c_{8} -108c_{1}^2c_{2}c_{7} +27c_{1}^2c_{3}c_{6} -3c_{1}^2c_{4}c_{5} +27c_{1}c_{2}^2c_{6} -6c_{1}c_{2}c_{3}c_{5} -c_{2}^3c_{5} +142c_{1}^2c_{9} -160c_{1}c_{2}c_{8} +76c_{1}c_{3}c_{7} -16c_{1}c_{4}c_{6} +4c_{1}c_{5}^2 +36c_{2}^2c_{7} -18c_{2}c_{3}c_{6} +2c_{2}c_{4}c_{5} +c_{3}^2c_{5} +262c_{1}c_{10} -74c_{2}c_{9} +110c_{3}c_{8} -23c_{4}c_{7} +21c_{5}c_{6} +292c_{11}) +T^12( -c_{1}^7c_{5} -10c_{1}^6c_{6} +6c_{1}^5c_{2}c_{5} -45c_{1}^5c_{7} +50c_{1}^4c_{2}c_{6} -5c_{1}^4c_{3}c_{5} -10c_{1}^3c_{2}^2c_{5} -120c_{1}^4c_{8} +180c_{1}^3c_{2}c_{7} -40c_{1}^3c_{3}c_{6} +4c_{1}^3c_{4}c_{5} -60c_{1}^2c_{2}^2c_{6} +12c_{1}^2c_{2}c_{3}c_{5} +4c_{1}c_{2}^3c_{5} -234c_{1}^3c_{9} +348c_{1}^2c_{2}c_{8} -141c_{1}^2c_{3}c_{7} +27c_{1}^2c_{4}c_{6} -6c_{1}^2c_{5}^2 -135c_{1}c_{2}^2c_{7} +60c_{1}c_{2}c_{3}c_{6} -6c_{1}c_{2}c_{4}c_{5} -3c_{1}c_{3}^2c_{5} +10c_{2}^3c_{6} -3c_{2}^2c_{3}c_{5} -532c_{1}^2c_{10} +320c_{1}c_{2}c_{9} -298c_{1}c_{3}c_{8} +61c_{1}c_{4}c_{7} -47c_{1}c_{5}c_{6} -112c_{2}^2c_{8} +94c_{2}c_{3}c_{7} -18c_{2}c_{4}c_{6} +4c_{2}c_{5}^2 -10c_{3}^2c_{6} +2c_{3}c_{4}c_{5} -1434c_{1}c_{11} -96c_{2}c_{10} -400c_{3}c_{9} +25c_{4}c_{8} -110c_{5}c_{7} -21c_{6}^2 -1640c_{12})
SSM-Thom polynomial in Schur functions T^5s_{5} +T^6( -5s_{6} -s_{5,1}) +T^7(15s_{7} +6s_{6,1} +s_{5,1,1}) +T^8( -s_{5,1,1,1} -7s_{6,1,1} -21s_{7,1} -35s_{8}) +T^9(s_{5,1,1,1,1} +8s_{6,1,1,1} +28s_{7,1,1} +56s_{8,1} +70s_{9}) +T^10( -s_{5,1,1,1,1,1} -s_{5,5} -9s_{6,1,1,1,1} -2s_{6,4} -36s_{7,1,1,1} -4s_{7,3} -84s_{8,1,1} -8s_{8,2} -142s_{9,1} -158s_{10}) +T^11(s_{5,1,1,1,1,1,1} +2s_{5,5,1} +10s_{6,1,1,1,1,1} +4s_{6,4,1} +19s_{6,5} +45s_{7,1,1,1,1} +8s_{7,3,1} +38s_{7,4} +120s_{8,1,1,1} +16s_{8,2,1} +76s_{8,3} +242s_{9,1,1} +152s_{9,2} +556s_{10,1} +690s_{11}) +T^12( -164s_{8,3,1} -390s_{8,4} -378s_{9,1,1,1} -328s_{9,2,1} -780s_{9,3} -1086s_{10,1,1} -1560s_{10,2} -3518s_{11,1} -4330s_{12} -65s_{6,6} -55s_{7,1,1,1,1,1} -12s_{7,3,1,1} -4s_{7,3,2} -82s_{7,4,1} -195s_{7,5} -165s_{8,1,1,1,1} -24s_{8,2,1,1} -8s_{8,2,2} -s_{5,5,2} -11s_{6,1,1,1,1,1,1} -6s_{6,4,1,1} -2s_{6,4,2} -41s_{6,5,1} -3s_{5,5,1,1} -s_{5,1,1,1,1,1,1,1})
SSM-Thom polynomial in Schur-tilde functions ( -3S_{7,3,1,1} -3S_{7,3,2} +5S_{7,4,1} +13S_{8,3,1} -5S_{8,4} -23S_{9,3} +S_{5,2,2,2,1} +S_{6,1,1,1,1,1,1} +S_{6,2,1,1,1,1} +S_{6,2,2,1,1} +S_{6,2,2,2} -79S_{10,2} -303S_{11,1} -351S_{12} +S_{5,1,1,1,1,1,1,1} +S_{5,2,1,1,1,1,1} +S_{5,2,2,1,1,1} +S_{7,1,1,1,1,1} +S_{7,2,1,1,1} +S_{7,2,2,1} +S_{8,1,1,1,1} -7S_{8,2,1,1} -7S_{8,2,2} -15S_{9,1,1,1} +33S_{9,2,1} +49S_{10,1,1} +S_{5,3,1,1,1,1} +S_{5,3,2,1,1} +S_{5,3,2,2} +S_{5,3,3,1} +S_{5,4,1,1,1} +S_{5,4,2,1} +S_{5,4,3} +S_{6,3,1,1,1} +S_{6,3,2,1} +S_{6,3,3} -S_{6,4,1,1} -S_{6,4,2} +2S_{6,5,1})T^12 +(S_{5,3,1,1,1} +S_{5,3,2,1} +S_{5,3,3} +S_{5,4,1,1} +S_{5,4,2} +129S_{11} +S_{6,3,1,1} +S_{6,3,2} -S_{6,4,1} +2S_{6,5} -3S_{7,3,1} +5S_{7,4} +13S_{8,3} +S_{5,1,1,1,1,1,1} +S_{5,2,1,1,1,1} +S_{5,2,2,1,1} +S_{5,2,2,2} +S_{6,1,1,1,1,1} +S_{6,2,1,1,1} +S_{6,2,2,1} +S_{7,1,1,1,1} +S_{7,2,1,1} +S_{7,2,2} +S_{8,1,1,1} -7S_{8,2,1} -15S_{9,1,1} +33S_{9,2} +81S_{10,1})T^11 +( -S_{6,4} -3S_{7,3} -7S_{8,2} -15S_{9,1} -31S_{10} +S_{5,1,1,1,1,1} +S_{5,2,1,1,1} +S_{5,2,2,1} +S_{5,3,1,1} +S_{5,3,2} +S_{5,4,1} +S_{6,1,1,1,1} +S_{6,2,1,1} +S_{6,2,2} +S_{6,3,1} +S_{7,1,1,1} +S_{7,2,1} +S_{8,1,1})T^10 +(S_{5,1,1,1,1} +S_{5,2,1,1} +S_{5,2,2} +S_{5,3,1} +S_{5,4} +S_{6,1,1,1} +S_{6,2,1} +S_{6,3} +S_{7,1,1} +S_{7,2} +S_{8,1} +S_{9})T^9 +(S_{5,1,1,1} +S_{5,2,1} +S_{5,3} +S_{6,1,1} +S_{6,2} +S_{7,1} +S_{8})T^8 +(S_{5,1,1} +S_{5,2} +S_{6,1} +S_{7})T^7 +(S_{5,1} +S_{6})T^6 +T^5S_{5}

codimension 10

Local algebra C[x]/(x^3)
Thom-Boardman class \Sigma^{1,1,0}
Codimension 10
SSM-Thom polynomial in Chern classes T^10(8c_{1}c_{9} +4c_{2}c_{8} +2c_{3}c_{7} +c_{4}c_{6} +c_{5}^2 +16c_{10}) +T^11( -16c_{1}^2c_{9} -8c_{1}c_{2}c_{8} -4c_{1}c_{3}c_{7} -2c_{1}c_{4}c_{6} -2c_{1}c_{5}^2 -136c_{1}c_{10} -52c_{2}c_{9} -26c_{3}c_{8} -13c_{4}c_{7} -13c_{5}c_{6} -208c_{11}) +T^12(24c_{1}^3c_{9} +12c_{1}^2c_{2}c_{8} +6c_{1}^2c_{3}c_{7} +3c_{1}^2c_{4}c_{6} +3c_{1}^2c_{5}^2 +280c_{1}^2c_{10} +100c_{1}c_{2}c_{9} +58c_{1}c_{3}c_{8} +29c_{1}c_{4}c_{7} +29c_{1}c_{5}c_{6} -8c_{2}^2c_{8} -4c_{2}c_{3}c_{7} -2c_{2}c_{4}c_{6} -2c_{2}c_{5}^2 +1224c_{1}c_{11} +348c_{2}c_{10} +190c_{3}c_{9} +95c_{4}c_{8} +66c_{5}c_{7} +29c_{6}^2 +1520c_{12})
SSM-Thom polynomial in Schur functions T^10(s_{5,5} +2s_{6,4} +4s_{7,3} +8s_{8,2} +16s_{9,1} +32s_{10}) +T^11( -2s_{5,5,1} -4s_{6,4,1} -19s_{6,5} -8s_{7,3,1} -38s_{7,4} -16s_{8,2,1} -76s_{8,3} -32s_{9,1,1} -152s_{9,2} -304s_{10,1} -480s_{11}) +T^12(3s_{5,5,1,1} +s_{5,5,2} +6s_{6,4,1,1} +2s_{6,4,2} +41s_{6,5,1} +63s_{6,6} +12s_{7,3,1,1} +4s_{7,3,2} +82s_{7,4,1} +195s_{7,5} +24s_{8,2,1,1} +8s_{8,2,2} +164s_{8,3,1} +390s_{8,4} +48s_{9,1,1,1} +328s_{9,2,1} +780s_{9,3} +624s_{10,1,1} +1560s_{10,2} +3056s_{11,1} +4000s_{12})
SSM-Thom polynomial in Schur-tilde functions (S_{5,5,1,1} +S_{5,5,2} +S_{7,5} +2S_{6,4,1,1} +2S_{6,4,2} -S_{6,5,1} +4S_{7,3,1,1} +4S_{7,3,2} -4S_{7,4,1} +8S_{8,2,1,1} +8S_{8,2,2} -12S_{8,3,1} +6S_{8,4} +16S_{9,1,1,1} -32S_{9,2,1} +24S_{9,3} -48S_{10,1,1} +80S_{10,2} +304S_{11,1} +352S_{12})T^12 +(S_{5,5,1} +2S_{6,4,1} -S_{6,5} +4S_{7,3,1} -4S_{7,4} +8S_{8,2,1} -12S_{8,3} +16S_{9,1,1} -32S_{9,2} -80S_{10,1} -128S_{11})T^11 +(2S_{6,4} +4S_{7,3} +8S_{8,2} +16S_{9,1} +32S_{10} +S_{5,5})T^10

codimension 12

Local algebra C[x,y]/(x^2,xy,y^2)
Thom-Boardman class \Sigma^{2,0}
Codimension 12
SSM-Thom polynomial in Chern classes T^12( -c_{5}c_{7} +c_{6}^2)
SSM-Thom polynomial in Schur functions T^12s_{6,6}
SSM-Thom polynomial in Schur-tilde functions T^12S_{6,6}