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SSM-Tp’s, l=3

SSM-Thom polynomials up to cohomological degree 24

of

contact singularities of relative dimension l=3 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^4c_{4} +T^5(c_{1}c_{4} +3c_{5}) +T^6( -c_{1}^2c_{4} -4c_{1}c_{5} +c_{2}c_{4} -6c_{6}) +T^7(c_{1}^3c_{4} +5c_{1}^2c_{5} -2c_{1}c_{2}c_{4} +10c_{1}c_{6} -5c_{2}c_{5} +c_{3}c_{4} +10c_{7}) +T^8( -c_{1}^4c_{4} -6c_{1}^3c_{5} +3c_{1}^2c_{2}c_{4} -15c_{1}^2c_{6} +12c_{1}c_{2}c_{5} -2c_{1}c_{3}c_{4} -c_{2}^2c_{4} -20c_{1}c_{7} +15c_{2}c_{6} -6c_{3}c_{5} +c_{4}^2 -15c_{8}) +T^9(c_{1}^5c_{4} +7c_{1}^4c_{5} -4c_{1}^3c_{2}c_{4} +21c_{1}^3c_{6} -21c_{1}^2c_{2}c_{5} +3c_{1}^2c_{3}c_{4} +3c_{1}c_{2}^2c_{4} +35c_{1}^2c_{7} -42c_{1}c_{2}c_{6} +14c_{1}c_{3}c_{5} -2c_{1}c_{4}^2 +7c_{2}^2c_{5} -2c_{2}c_{3}c_{4} +35c_{1}c_{8} -35c_{2}c_{7} +21c_{3}c_{6} -6c_{4}c_{5} +21c_{9}) +T^10( -c_{1}^6c_{4} -8c_{1}^5c_{5} +5c_{1}^4c_{2}c_{4} -28c_{1}^4c_{6} +32c_{1}^3c_{2}c_{5} -4c_{1}^3c_{3}c_{4} -6c_{1}^2c_{2}^2c_{4} -56c_{1}^3c_{7} +84c_{1}^2c_{2}c_{6} -24c_{1}^2c_{3}c_{5} +3c_{1}^2c_{4}^2 -24c_{1}c_{2}^2c_{5} +6c_{1}c_{2}c_{3}c_{4} +c_{2}^3c_{4} -70c_{1}^2c_{8} +112c_{1}c_{2}c_{7} -56c_{1}c_{3}c_{6} +14c_{1}c_{4}c_{5} -28c_{2}^2c_{6} +16c_{2}c_{3}c_{5} -2c_{2}c_{4}^2 -c_{3}^2c_{4} -56c_{1}c_{9} +70c_{2}c_{8} -56c_{3}c_{7} +28c_{4}c_{6} -7c_{5}^2 -28c_{10}) +T^11(c_{1}^7c_{4} +9c_{1}^6c_{5} -6c_{1}^5c_{2}c_{4} +36c_{1}^5c_{6} -45c_{1}^4c_{2}c_{5} +5c_{1}^4c_{3}c_{4} +10c_{1}^3c_{2}^2c_{4} +84c_{1}^4c_{7} -144c_{1}^3c_{2}c_{6} +36c_{1}^3c_{3}c_{5} -4c_{1}^3c_{4}^2 +54c_{1}^2c_{2}^2c_{5} -12c_{1}^2c_{2}c_{3}c_{4} -4c_{1}c_{2}^3c_{4} +126c_{1}^3c_{8} -252c_{1}^2c_{2}c_{7} +108c_{1}^2c_{3}c_{6} -24c_{1}^2c_{4}c_{5} +108c_{1}c_{2}^2c_{6} -54c_{1}c_{2}c_{3}c_{5} +6c_{1}c_{2}c_{4}^2 +3c_{1}c_{3}^2c_{4} -9c_{2}^3c_{5} +3c_{2}^2c_{3}c_{4} +126c_{1}^2c_{9} -252c_{1}c_{2}c_{8} +168c_{1}c_{3}c_{7} -72c_{1}c_{4}c_{6} +16c_{1}c_{5}^2 +84c_{2}^2c_{7} -72c_{2}c_{3}c_{6} +16c_{2}c_{4}c_{5} +9c_{3}^2c_{5} -2c_{3}c_{4}^2 +84c_{1}c_{10} -126c_{2}c_{9} +126c_{3}c_{8} -80c_{4}c_{7} +24c_{5}c_{6} +36c_{11}) +T^12( -c_{1}^8c_{4} -10c_{1}^7c_{5} +7c_{1}^6c_{2}c_{4} -45c_{1}^6c_{6} +60c_{1}^5c_{2}c_{5} -6c_{1}^5c_{3}c_{4} -15c_{1}^4c_{2}^2c_{4} -120c_{1}^5c_{7} +225c_{1}^4c_{2}c_{6} -50c_{1}^4c_{3}c_{5} +5c_{1}^4c_{4}^2 -100c_{1}^3c_{2}^2c_{5} +20c_{1}^3c_{2}c_{3}c_{4} +10c_{1}^2c_{2}^3c_{4} -210c_{1}^4c_{8} +480c_{1}^3c_{2}c_{7} -180c_{1}^3c_{3}c_{6} +36c_{1}^3c_{4}c_{5} -270c_{1}^2c_{2}^2c_{6} +120c_{1}^2c_{2}c_{3}c_{5} -12c_{1}^2c_{2}c_{4}^2 -6c_{1}^2c_{3}^2c_{4} +40c_{1}c_{2}^3c_{5} -12c_{1}c_{2}^2c_{3}c_{4} -c_{2}^4c_{4} -252c_{1}^3c_{9} +630c_{1}^2c_{2}c_{8} -360c_{1}^2c_{3}c_{7} +135c_{1}^2c_{4}c_{6} -27c_{1}^2c_{5}^2 -360c_{1}c_{2}^2c_{7} +270c_{1}c_{2}c_{3}c_{6} -54c_{1}c_{2}c_{4}c_{5} -30c_{1}c_{3}^2c_{5} +6c_{1}c_{3}c_{4}^2 +45c_{2}^3c_{6} -30c_{2}^2c_{3}c_{5} +3c_{2}^2c_{4}^2 +3c_{2}c_{3}^2c_{4} -210c_{1}^2c_{10} +504c_{1}c_{2}c_{9} -420c_{1}c_{3}c_{8} +231c_{1}c_{4}c_{7} -63c_{1}c_{5}c_{6} -210c_{2}^2c_{8} +240c_{2}c_{3}c_{7} -90c_{2}c_{4}c_{6} +18c_{2}c_{5}^2 -45c_{3}^2c_{6} +18c_{3}c_{4}c_{5} -c_{4}^3 -120c_{1}c_{11} +210c_{2}c_{10} -252c_{3}c_{9} +204c_{4}c_{8} -123c_{5}c_{7} +45c_{6}^2 -45c_{12})
SSM-Thom polynomial in Schur functions -T^4s_{4} +s_{0} +T^5(4s_{5} +s_{4,1}) +T^6( -10s_{6} -5s_{5,1} -s_{4,1,1}) +T^7(20s_{7} +15s_{6,1} +6s_{5,1,1} +s_{4,1,1,1}) +T^8( -s_{4,1,1,1,1} -7s_{5,1,1,1} -21s_{6,1,1} -35s_{7,1} -35s_{8}) +T^9(s_{4,1,1,1,1,1} +8s_{5,1,1,1,1} +28s_{6,1,1,1} +56s_{7,1,1} +70s_{8,1} +56s_{9}) +T^10( -9s_{5,1,1,1,1,1} +s_{5,5} -36s_{6,1,1,1,1} -84s_{7,1,1,1} -126s_{8,1,1} -126s_{9,1} -84s_{10} -s_{4,1,1,1,1,1,1}) +T^11(s_{4,1,1,1,1,1,1,1} +10s_{5,1,1,1,1,1,1} -2s_{5,5,1} +45s_{6,1,1,1,1,1} -5s_{6,5} +120s_{7,1,1,1,1} +210s_{8,1,1,1} +252s_{9,1,1} +210s_{10,1} +120s_{11}) +T^12( -s_{4,1,1,1,1,1,1,1,1} -11s_{5,1,1,1,1,1,1,1} +3s_{5,5,1,1} +s_{5,5,2} -55s_{6,1,1,1,1,1,1} +11s_{6,5,1} +10s_{6,6} -165s_{7,1,1,1,1,1} +15s_{7,5} -330s_{8,1,1,1,1} -462s_{9,1,1,1} -462s_{10,1,1} -330s_{11,1} -165s_{12})
SSM-Thom polynomial in Schur-tilde functions (S_{2,2,2,2,1,1,1,1} +S_{2,2,2,2,2,1,1} +S_{2,2,2,2,2,2} +S_{3,1,1,1,1,1,1,1,1,1} +S_{3,2,1,1,1,1,1,1,1} +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} +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_{2,2,1,1,1,1,1,1,1,1} +S_{2,2,2,1,1,1,1,1,1})T^12 +(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_{1,1,1,1,1,1,1,1,1,1,1} +S_{2,1,1,1,1,1,1,1,1,1} +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_{3,1,1,1,1,1,1,1,1} +S_{3,2,1,1,1,1,1,1} +S_{3,2,2,1,1,1,1})T^11 +(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_{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})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})T^9 +(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})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})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_{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})T^5 +(S_{1,1,1,1} +S_{2,1,1} +S_{3,1} +S_{2,2})T^4 +(S_{1,1,1} +S_{2,1} +S_{3})T^3 +(S_{2} +S_{1,1})T^2 +TS_{1} +S_{}

codimension 4

Local algebra C[x]/(x^2)
Thom-Boardman class \Sigma^{1,0}
Codimension 4
SSM-Thom polynomial in Chern classes T^4c_{4} +T^5( -c_{1}c_{4} -3c_{5}) +T^6(c_{1}^2c_{4} +4c_{1}c_{5} -c_{2}c_{4} +6c_{6}) +T^7( -c_{1}^3c_{4} -5c_{1}^2c_{5} +2c_{1}c_{2}c_{4} -10c_{1}c_{6} +5c_{2}c_{5} -c_{3}c_{4} -10c_{7}) +T^8(c_{1}^4c_{4} +6c_{1}^3c_{5} -3c_{1}^2c_{2}c_{4} +15c_{1}^2c_{6} -12c_{1}c_{2}c_{5} +2c_{1}c_{3}c_{4} +c_{2}^2c_{4} +16c_{1}c_{7} -17c_{2}c_{6} +5c_{3}c_{5} -2c_{4}^2 +7c_{8}) +T^9( -c_{1}^5c_{4} -7c_{1}^4c_{5} +4c_{1}^3c_{2}c_{4} -21c_{1}^3c_{6} +21c_{1}^2c_{2}c_{5} -3c_{1}^2c_{3}c_{4} -3c_{1}c_{2}^2c_{4} -27c_{1}^2c_{7} +46c_{1}c_{2}c_{6} -12c_{1}c_{3}c_{5} +4c_{1}c_{4}^2 -7c_{2}^2c_{5} +2c_{2}c_{3}c_{4} +21c_{1}c_{8} +55c_{2}c_{7} -11c_{3}c_{6} +16c_{4}c_{5} +59c_{9}) +T^10(c_{1}^6c_{4} +8c_{1}^5c_{5} -5c_{1}^4c_{2}c_{4} +28c_{1}^4c_{6} -32c_{1}^3c_{2}c_{5} +4c_{1}^3c_{3}c_{4} +6c_{1}^2c_{2}^2c_{4} +44c_{1}^3c_{7} -90c_{1}^2c_{2}c_{6} +21c_{1}^2c_{3}c_{5} -6c_{1}^2c_{4}^2 +24c_{1}c_{2}^2c_{5} -6c_{1}c_{2}c_{3}c_{4} -c_{2}^3c_{4} -46c_{1}^2c_{8} -150c_{1}c_{2}c_{7} +33c_{1}c_{3}c_{6} -37c_{1}c_{4}c_{5} +32c_{2}^2c_{6} -14c_{2}c_{3}c_{5} +4c_{2}c_{4}^2 +c_{3}^2c_{4} -360c_{1}c_{9} -170c_{2}c_{8} -2c_{3}c_{7} -68c_{4}c_{6} -11c_{5}^2 -436c_{10}) +T^11( -c_{1}^7c_{4} -9c_{1}^6c_{5} +6c_{1}^5c_{2}c_{4} -36c_{1}^5c_{6} +45c_{1}^4c_{2}c_{5} -5c_{1}^4c_{3}c_{4} -10c_{1}^3c_{2}^2c_{4} -68c_{1}^4c_{7} +152c_{1}^3c_{2}c_{6} -32c_{1}^3c_{3}c_{5} +8c_{1}^3c_{4}^2 -54c_{1}^2c_{2}^2c_{5} +12c_{1}^2c_{2}c_{3}c_{4} +4c_{1}c_{2}^3c_{4} +62c_{1}^3c_{8} +306c_{1}^2c_{2}c_{7} -69c_{1}^2c_{3}c_{6} +63c_{1}^2c_{4}c_{5} -120c_{1}c_{2}^2c_{6} +48c_{1}c_{2}c_{3}c_{5} -12c_{1}c_{2}c_{4}^2 -3c_{1}c_{3}^2c_{4} +9c_{2}^3c_{5} -3c_{2}^2c_{3}c_{4} +790c_{1}^2c_{9} +402c_{1}c_{2}c_{8} -9c_{1}c_{3}c_{7} +176c_{1}c_{4}c_{6} +31c_{1}c_{5}^2 -136c_{2}^2c_{7} +50c_{2}c_{3}c_{6} -42c_{2}c_{4}c_{5} -7c_{3}^2c_{5} +4c_{3}c_{4}^2 +2148c_{1}c_{10} +430c_{2}c_{9} +146c_{3}c_{8} +228c_{4}c_{7} +84c_{5}c_{6} +2012c_{11}) +T^12(c_{1}^8c_{4} +10c_{1}^7c_{5} -7c_{1}^6c_{2}c_{4} +45c_{1}^6c_{6} -60c_{1}^5c_{2}c_{5} +6c_{1}^5c_{3}c_{4} +15c_{1}^4c_{2}^2c_{4} +100c_{1}^5c_{7} -235c_{1}^4c_{2}c_{6} +45c_{1}^4c_{3}c_{5} -10c_{1}^4c_{4}^2 +100c_{1}^3c_{2}^2c_{5} -20c_{1}^3c_{2}c_{3}c_{4} -10c_{1}^2c_{2}^3c_{4} -62c_{1}^4c_{8} -548c_{1}^3c_{2}c_{7} +122c_{1}^3c_{3}c_{6} -94c_{1}^3c_{4}c_{5} +294c_{1}^2c_{2}^2c_{6} -108c_{1}^2c_{2}c_{3}c_{5} +24c_{1}^2c_{2}c_{4}^2 +6c_{1}^2c_{3}^2c_{4} -40c_{1}c_{2}^3c_{5} +12c_{1}c_{2}^2c_{3}c_{4} +c_{2}^4c_{4} -1356c_{1}^3c_{9} -758c_{1}^2c_{2}c_{8} +50c_{1}^2c_{3}c_{7} -332c_{1}^2c_{4}c_{6} -62c_{1}^2c_{5}^2 +522c_{1}c_{2}^2c_{7} -195c_{1}c_{2}c_{3}c_{6} +141c_{1}c_{2}c_{4}c_{5} +24c_{1}c_{3}^2c_{5} -12c_{1}c_{3}c_{4}^2 -51c_{2}^3c_{6} +27c_{2}^2c_{3}c_{5} -6c_{2}^2c_{4}^2 -3c_{2}c_{3}^2c_{4} -5058c_{1}^2c_{10} -534c_{1}c_{2}c_{9} -489c_{1}c_{3}c_{8} -653c_{1}c_{4}c_{7} -252c_{1}c_{5}c_{6} +568c_{2}^2c_{8} -107c_{2}c_{3}c_{7} +226c_{2}c_{4}c_{6} +41c_{2}c_{5}^2 +16c_{3}^2c_{6} -45c_{3}c_{4}c_{5} +3c_{4}^3 -9660c_{1}c_{11} -592c_{2}c_{10} -935c_{3}c_{9} -698c_{4}c_{8} -191c_{5}c_{7} -176c_{6}^2 -7595c_{12})
SSM-Thom polynomial in Schur functions T^4s_{4} +T^5( -4s_{5} -s_{4,1}) +T^6(10s_{6} +5s_{5,1} +s_{4,1,1}) +T^7( -20s_{7} -15s_{6,1} -6s_{5,1,1} -s_{4,1,1,1}) +T^8(s_{4,1,1,1,1} -s_{4,4} +7s_{5,1,1,1} -2s_{5,3} +21s_{6,1,1} -4s_{6,2} +27s_{7,1} +19s_{8}) +T^9( -s_{4,1,1,1,1,1} +2s_{4,4,1} -8s_{5,1,1,1,1} +4s_{5,3,1} +16s_{5,4} -28s_{6,1,1,1} +8s_{6,2,1} +32s_{6,3} -40s_{7,1,1} +64s_{7,2} +58s_{8,1} +136s_{9}) +T^10(9s_{5,1,1,1,1,1} -6s_{5,3,1,1} -2s_{5,3,2} -35s_{5,4,1} -47s_{5,5} +36s_{6,1,1,1,1} -12s_{6,2,1,1} -4s_{6,2,2} -70s_{6,3,1} -140s_{6,4} +60s_{7,1,1,1} -140s_{7,2,1} -280s_{7,3} -138s_{8,1,1} -560s_{8,2} -962s_{9,1} -1228s_{10} +s_{4,1,1,1,1,1,1} -3s_{4,4,1,1} -s_{4,4,2}) +T^11(214s_{8,1,1,1} +1332s_{8,2,1} +1780s_{8,3} +2108s_{9,1,1} +3560s_{9,2} +6430s_{10,1} +6600s_{11} +16s_{6,2,1,1,1} +8s_{6,2,2,1} +114s_{6,3,1,1} +38s_{6,3,2} +333s_{6,4,1} +395s_{6,5} -88s_{7,1,1,1,1} +228s_{7,2,1,1} +76s_{7,2,2} +666s_{7,3,1} +890s_{7,4} -10s_{5,1,1,1,1,1,1} +8s_{5,3,1,1,1} +4s_{5,3,2,1} +57s_{5,4,1,1} +19s_{5,4,2} +111s_{5,5,1} -45s_{6,1,1,1,1,1} +4s_{4,4,1,1,1} +2s_{4,4,2,1} -s_{4,1,1,1,1,1,1,1}) +T^12( -4578s_{8,3,1} -4605s_{8,4} -3602s_{9,1,1,1} -9156s_{9,2,1} -9210s_{9,3} -14794s_{10,1,1} -18420s_{10,2} -32510s_{11,1} -28555s_{12} -670s_{6,6} +125s_{7,1,1,1,1,1} -328s_{7,2,1,1,1} -164s_{7,2,2,1} -1172s_{7,3,1,1} -390s_{7,3,2} -2289s_{7,4,1} -2210s_{7,5} -278s_{8,1,1,1,1} -2344s_{8,2,1,1} -780s_{8,2,2} -65s_{5,5,2} +55s_{6,1,1,1,1,1,1} -20s_{6,2,1,1,1,1} -12s_{6,2,2,1,1} -4s_{6,2,2,2} -164s_{6,3,1,1,1} -82s_{6,3,2,1} -586s_{6,4,1,1} -195s_{6,4,2} -1012s_{6,5,1} -10s_{5,3,1,1,1,1} -6s_{5,3,2,1,1} -2s_{5,3,2,2} -82s_{5,4,1,1,1} -41s_{5,4,2,1} -194s_{5,5,1,1} -5s_{4,4,1,1,1,1} -3s_{4,4,2,1,1} -s_{4,4,2,2} +11s_{5,1,1,1,1,1,1,1} +s_{4,1,1,1,1,1,1,1,1})
SSM-Thom polynomial in Schur-tilde functions ( -5S_{7,3,1,1} -13S_{7,3,2} +2S_{7,4,1} -7S_{8,3,1} -41S_{9,3} +S_{5,2,2,2,1} +S_{6,1,1,1,1,1,1} -3S_{6,2,1,1,1,1} -3S_{6,2,2,1,1} -3S_{6,2,2,2} +69S_{10,2} -631S_{11,1} -351S_{12} +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_{5,1,1,1,1,1,1,1} +S_{5,2,1,1,1,1,1} +S_{5,2,2,1,1,1} -7S_{7,1,1,1,1,1} +13S_{7,2,1,1,1} +5S_{7,2,2,1} +17S_{8,1,1,1,1} -39S_{8,2,1,1} +9S_{8,2,2} -31S_{9,1,1,1} +121S_{9,2,1} -143S_{10,1,1} +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_{5,3,1,1,1,1} -S_{5,3,2,1,1} -S_{5,3,2,2} -S_{5,3,3,1} +2S_{5,4,1,1,1} +2S_{5,4,2,1} +2S_{5,4,3} +5S_{6,3,1,1,1} +5S_{6,3,2,1} +S_{6,3,3})T^12 +(S_{4,3,2,2} +S_{4,3,3,1} -S_{5,3,1,1,1} -S_{5,3,2,1} -S_{5,3,3} +2S_{5,4,1,1} +2S_{5,4,2} +209S_{11} +S_{4,2,2,2,1} +S_{4,3,1,1,1,1} +S_{4,3,2,1,1} +5S_{6,3,1,1} +5S_{6,3,2} -5S_{7,3,1} +2S_{7,4} +9S_{8,3} +S_{4,2,2,1,1,1} +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} -3S_{6,2,1,1,1} -3S_{6,2,2,1} -7S_{7,1,1,1,1} +13S_{7,2,1,1} +5S_{7,2,2} +17S_{8,1,1,1} -39S_{8,2,1} +S_{9,1,1} +9S_{9,2} +289S_{10,1} +S_{4,1,1,1,1,1,1,1} +S_{4,2,1,1,1,1,1})T^11 +(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_{5,1,1,1,1,1} +S_{5,2,1,1,1} +S_{5,2,2,1} +S_{6,1,1,1,1} -S_{5,3,1,1} -S_{5,3,2} +2S_{5,4,1} -3S_{6,2,1,1} -3S_{6,2,2} +5S_{6,3,1} -7S_{7,1,1,1} +13S_{7,2,1} -5S_{7,3} +17S_{8,1,1} -23S_{8,2} -111S_{9,1} -111S_{10})T^10 +( -S_{5,3,1} +2S_{5,4} -3S_{6,2,1} +5S_{6,3} -7S_{7,1,1} +13S_{7,2} +33S_{8,1} +49S_{9} +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_{5,1,1,1,1} +S_{5,2,1,1} +S_{5,2,2} +S_{6,1,1,1})T^9 +( -S_{5,3} -3S_{6,2} -7S_{7,1} -15S_{8} +S_{4,1,1,1,1} +S_{4,2,1,1} +S_{4,2,2} +S_{4,3,1} +S_{5,1,1,1} +S_{5,2,1} +S_{6,1,1})T^8 +(S_{4,3} +S_{4,1,1,1} +S_{4,2,1} +S_{5,1,1} +S_{5,2} +S_{6,1} +S_{7})T^7 +(S_{4,1,1} +S_{4,2} +S_{5,1} +S_{6})T^6 +(S_{4,1} +S_{5})T^5 +T^4S_{4}

codimension 8

Local algebra C[x]/(x^3)
Thom-Boardman class \Sigma^{1,1,0}
Codimension 8
SSM-Thom polynomial in Chern classes T^8(4c_{1}c_{7} +2c_{2}c_{6} +c_{3}c_{5} +c_{4}^2 +8c_{8}) +T^9( -8c_{1}^2c_{7} -4c_{1}c_{2}c_{6} -2c_{1}c_{3}c_{5} -2c_{1}c_{4}^2 -56c_{1}c_{8} -20c_{2}c_{7} -10c_{3}c_{6} -10c_{4}c_{5} -80c_{9}) +T^10(12c_{1}^3c_{7} +6c_{1}^2c_{2}c_{6} +3c_{1}^2c_{3}c_{5} +3c_{1}^2c_{4}^2 +116c_{1}^2c_{8} +38c_{1}c_{2}c_{7} +23c_{1}c_{3}c_{6} +23c_{1}c_{4}c_{5} -4c_{2}^2c_{6} -2c_{2}c_{3}c_{5} -2c_{2}c_{4}^2 +416c_{1}c_{9} +100c_{2}c_{8} +58c_{3}c_{7} +41c_{4}c_{6} +17c_{5}^2 +464c_{10}) +T^11( -16c_{1}^4c_{7} -8c_{1}^3c_{2}c_{6} -4c_{1}^3c_{3}c_{5} -4c_{1}^3c_{4}^2 -188c_{1}^3c_{8} -54c_{1}^2c_{2}c_{7} -39c_{1}^2c_{3}c_{6} -39c_{1}^2c_{4}c_{5} +12c_{1}c_{2}^2c_{6} +6c_{1}c_{2}c_{3}c_{5} +6c_{1}c_{2}c_{4}^2 -916c_{1}^2c_{9} -150c_{1}c_{2}c_{8} -159c_{1}c_{3}c_{7} -106c_{1}c_{4}c_{6} -45c_{1}c_{5}^2 +52c_{2}^2c_{7} +22c_{2}c_{3}c_{6} +26c_{2}c_{4}c_{5} -2c_{3}^2c_{5} -2c_{3}c_{4}^2 -2232c_{1}c_{10} -304c_{2}c_{9} -272c_{3}c_{8} -151c_{4}c_{7} -105c_{5}c_{6} -2048c_{11}) +T^12(20c_{1}^5c_{7} +10c_{1}^4c_{2}c_{6} +5c_{1}^4c_{3}c_{5} +5c_{1}^4c_{4}^2 +272c_{1}^4c_{8} +68c_{1}^3c_{2}c_{7} +58c_{1}^3c_{3}c_{6} +58c_{1}^3c_{4}c_{5} -24c_{1}^2c_{2}^2c_{6} -12c_{1}^2c_{2}c_{3}c_{5} -12c_{1}^2c_{2}c_{4}^2 +1608c_{1}^3c_{9} +128c_{1}^2c_{2}c_{8} +310c_{1}^2c_{3}c_{7} +200c_{1}^2c_{4}c_{6} +86c_{1}^2c_{5}^2 -162c_{1}c_{2}^2c_{7} -75c_{1}c_{2}c_{3}c_{6} -87c_{1}c_{2}c_{4}c_{5} +6c_{1}c_{3}^2c_{5} +6c_{1}c_{3}c_{4}^2 +6c_{2}^3c_{6} +3c_{2}^2c_{3}c_{5} +3c_{2}^2c_{4}^2 +5196c_{1}^2c_{10} -30c_{1}c_{2}c_{9} +883c_{1}c_{3}c_{8} +412c_{1}c_{4}c_{7} +303c_{1}c_{5}c_{6} -370c_{2}^2c_{8} -143c_{2}c_{3}c_{7} -145c_{2}c_{4}c_{6} -58c_{2}c_{5}^2 +27c_{3}^2c_{6} +24c_{3}c_{4}c_{5} -3c_{4}^3 +9420c_{1}c_{11} +226c_{2}c_{10} +1117c_{3}c_{9} +458c_{4}c_{8} +293c_{5}c_{7} +126c_{6}^2 +7208c_{12})
SSM-Thom polynomial in Schur functions T^8(s_{4,4} +2s_{5,3} +4s_{6,2} +8s_{7,1} +16s_{8}) +T^9( -2s_{4,4,1} -4s_{5,3,1} -16s_{5,4} -8s_{6,2,1} -32s_{6,3} -16s_{7,1,1} -64s_{7,2} -128s_{8,1} -192s_{9}) +T^10(3s_{4,4,1,1} +s_{4,4,2} +6s_{5,3,1,1} +2s_{5,3,2} +35s_{5,4,1} +45s_{5,5} +12s_{6,2,1,1} +4s_{6,2,2} +70s_{6,3,1} +140s_{6,4} +24s_{7,1,1,1} +140s_{7,2,1} +280s_{7,3} +264s_{8,1,1} +560s_{8,2} +1088s_{9,1} +1312s_{10}) +T^11( -424s_{8,1,1,1} -1332s_{8,2,1} -1780s_{8,3} -2360s_{9,1,1} -3560s_{9,2} -6640s_{10,1} -6720s_{11} -16s_{6,2,1,1,1} -8s_{6,2,2,1} -114s_{6,3,1,1} -38s_{6,3,2} -333s_{6,4,1} -385s_{6,5} -32s_{7,1,1,1,1} -228s_{7,2,1,1} -76s_{7,2,2} -666s_{7,3,1} -890s_{7,4} -8s_{5,3,1,1,1} -4s_{5,3,2,1} -57s_{5,4,1,1} -19s_{5,4,2} -107s_{5,5,1} -4s_{4,4,1,1,1} -2s_{4,4,2,1}) +T^12(4464s_{8,3,1} +4394s_{8,4} +4064s_{9,1,1,1} +8976s_{9,2,1} +8820s_{9,3} +15040s_{10,1,1} +17736s_{10,2} +31760s_{11,1} +27424s_{12} +626s_{6,6} +40s_{7,1,1,1,1,1} +328s_{7,2,1,1,1} +164s_{7,2,2,1} +1172s_{7,3,1,1} +360s_{7,3,2} +2224s_{7,4,1} +2091s_{7,5} +608s_{8,1,1,1,1} +2344s_{8,2,1,1} +744s_{8,2,2} +58s_{5,5,2} +20s_{6,2,1,1,1,1} +12s_{6,2,2,1,1} +4s_{6,2,2,2} +164s_{6,3,1,1,1} +82s_{6,3,2,1} -6s_{6,3,3} +586s_{6,4,1,1} +176s_{6,4,2} +966s_{6,5,1} +10s_{5,3,1,1,1,1} +6s_{5,3,2,1,1} +2s_{5,3,2,2} +82s_{5,4,1,1,1} +41s_{5,4,2,1} -5s_{5,4,3} +188s_{5,5,1,1} +5s_{4,4,1,1,1,1} +3s_{4,4,2,1,1} +s_{4,4,2,2} -s_{4,4,4})
SSM-Thom polynomial in Schur-tilde functions (6S_{7,3,1,1} -16S_{7,3,2} -66S_{7,4,1} -89S_{7,5} -106S_{8,3,1} -210S_{8,4} -348S_{9,3} +4S_{6,2,1,1,1,1} +4S_{6,2,2,1,1} +4S_{6,2,2,2} -752S_{10,2} -448S_{11,1} -944S_{12} +8S_{7,1,1,1,1,1} -12S_{7,2,1,1,1} -4S_{7,2,2,1} -16S_{8,1,1,1,1} +40S_{8,2,1,1} -44S_{8,2,2} +32S_{9,1,1,1} -300S_{9,2,1} -72S_{10,1,1} +S_{4,4,1,1,1,1} +S_{4,4,2,1,1} +S_{4,4,2,2} +S_{4,4,3,1} +2S_{5,3,1,1,1,1} +2S_{5,3,2,1,1} +2S_{5,3,2,2} +2S_{5,3,3,1} -S_{5,4,1,1,1} -S_{5,4,2,1} -6S_{5,4,3} -5S_{5,5,2} -4S_{6,3,1,1,1} -4S_{6,3,2,1} -6S_{6,3,3} +S_{6,4,1,1} -18S_{6,4,2} -24S_{6,5,1} -24S_{6,6})T^12 +(2S_{5,3,1,1,1} +2S_{5,3,2,1} +2S_{5,3,3} -S_{5,4,1,1} -S_{5,4,2} +4S_{6,2,1,1,1} +4S_{6,2,2,1} -4S_{6,3,1,1} -4S_{6,3,2} +8S_{7,1,1,1,1} -12S_{7,2,1,1} -4S_{7,2,2} +6S_{7,3,1} -S_{7,4} -16S_{8,1,1,1} +40S_{8,2,1} -8S_{8,3} -8S_{9,2} -288S_{10,1} -208S_{11} +S_{4,4,1,1,1} +S_{4,4,2,1} +S_{4,4,3} +S_{6,4,1})T^11 +(2S_{5,3,1,1} +2S_{5,3,2} -S_{5,4,1} +4S_{6,2,1,1} +4S_{6,2,2} -4S_{6,3,1} +8S_{7,1,1,1} -12S_{7,2,1} +6S_{7,3} -16S_{8,1,1} +24S_{8,2} +112S_{9,1} +112S_{10} +S_{4,4,1,1} +S_{4,4,2} +S_{6,4})T^10 +(2S_{5,3,1} -S_{5,4} +4S_{6,2,1} -4S_{6,3} +8S_{7,1,1} -12S_{7,2} -32S_{8,1} -48S_{9} +S_{4,4,1})T^9 +(S_{4,4} +2S_{5,3} +4S_{6,2} +8S_{7,1} +16S_{8})T^8

codimension 10

Local algebra C[x,y]/(x^2,xy,y^2)
Thom-Boardman class \Sigma^{2,0}
Codimension 10
SSM-Thom polynomial in Chern classes T^10( -c_{4}c_{6} +c_{5}^2) +T^11(2c_{1}c_{4}c_{6} -2c_{1}c_{5}^2 +3c_{4}c_{7} -3c_{5}c_{6}) +T^12( -3c_{1}^2c_{4}c_{6} +3c_{1}^2c_{5}^2 -7c_{1}c_{4}c_{7} +7c_{1}c_{5}c_{6} +2c_{2}c_{4}c_{6} -2c_{2}c_{5}^2 -7c_{4}c_{8} +7c_{5}c_{7})
SSM-Thom polynomial in Schur functions T^12(s_{4,4,4} +5s_{5,4,3} +5s_{5,5,2} +6s_{6,3,3} +19s_{6,4,2} +24s_{6,5,1} +24s_{6,6} +30s_{7,3,2} +65s_{7,4,1} +89s_{7,5} +36s_{8,2,2} +114s_{8,3,1} +211s_{8,4} +180s_{9,2,1} +390s_{9,3} +216s_{10,1,1} +684s_{10,2} +1080s_{11,1} +1296s_{12})
SSM-Thom polynomial in Schur-tilde functions (1296S_{12} +S_{4,4,4} +5S_{5,4,3} +5S_{5,5,2} +6S_{6,3,3} +19S_{6,4,2} +24S_{6,5,1} +24S_{6,6} +30S_{7,3,2} +65S_{7,4,1} +89S_{7,5} +36S_{8,2,2} +114S_{8,3,1} +211S_{8,4} +180S_{9,2,1} +390S_{9,3} +216S_{10,1,1} +684S_{10,2} +1080S_{11,1})T^12

codimension 12

Local algebra C[x]/(x^4)
Thom-Boardman class \Sigma^{1,1,1,1,0}
Codimension 12
SSM-Thom polynomial in Chern classes T^12(72c_{1}^2c_{10} +60c_{1}c_{2}c_{9} +26c_{1}c_{3}c_{8} +17c_{1}c_{4}c_{7} +5c_{1}c_{5}c_{6} +12c_{2}^2c_{8} +10c_{2}c_{3}c_{7} +7c_{2}c_{4}c_{6} +c_{2}c_{5}^2 +2c_{3}^2c_{6} +3c_{3}c_{4}c_{5} +c_{4}^3 +360c_{1}c_{11} +156c_{2}c_{10} +70c_{3}c_{9} +43c_{4}c_{8} +14c_{5}c_{7} +5c_{6}^2 +432c_{12})
SSM-Thom polynomial in Schur functions T^12(s_{4,4,4} +5s_{5,4,3} +5s_{5,5,2} +6s_{6,3,3} +19s_{6,4,2} +24s_{6,5,1} +24s_{6,6} +30s_{7,3,2} +65s_{7,4,1} +89s_{7,5} +36s_{8,2,2} +114s_{8,3,1} +211s_{8,4} +180s_{9,2,1} +390s_{9,3} +216s_{10,1,1} +684s_{10,2} +1080s_{11,1} +1296s_{12})
SSM-Thom polynomial in Schur-tilde functions (1296S_{12} +S_{4,4,4} +5S_{5,4,3} +5S_{5,5,2} +6S_{6,3,3} +19S_{6,4,2} +24S_{6,5,1} +24S_{6,6} +30S_{7,3,2} +65S_{7,4,1} +89S_{7,5} +36S_{8,2,2} +114S_{8,3,1} +211S_{8,4} +180S_{9,2,1} +390S_{9,3} +216S_{10,1,1} +684S_{10,2} +1080S_{11,1})T^12