Hopf cocycle in terms of the Monomial bases for the smash product decomposition of SSym evaluated on the monomial basis of QSym

Cocycle of total degree 0
sigma(M(), M())     =     M0
Cocycle of total degree 2
sigma(M(1), M(1))    =     0.
Cocycles of total degree 3
sigma(M(1), M(2))    =     2M213.
sigma(M(1), M(11))    =     M132.
sigma(M(2), M(1))    =     2M132.
sigma(M(11), M(1))    =     M213.
Cocycles of total degree 4
sigma(M(1), M(3))    =     2M2134 + M2314 + M3124.
sigma(M(1), M(21))    =     -2M2134 + M1342 -4M2143-2M2413 -M3142-2M4213.
sigma(M(1), M(12))    =     M1423 + M2413 + 2M4213.
sigma(M(1), M(111))    =     -M1324-M1342 -M1423-2M1432.
sigma(M(2), M(2))    =     2M1324 + M1342 + M1423 + M2314 + M3124 + M2413 + M3142.
sigma(M(2), M(11))    =     M1243-2M1324 -M1342-M1423 -3M1432.
sigma(M(11), M(2))    =     -M2134-4M2143 + M2314 + M3124 -2M2413-2M3142 + 3M3214.
sigma(M(11), M(11))    =     -M1324-M2134 -M1342-M1423 -M2143-3M1432.
sigma(M(3), M(1))    =     2M1243 + M1342 + M1423.
sigma(M(21), M(1))    =     -2M1324-2M1342 -2M1423 + M2314 -6M1432 + M2413 -2M4132.
sigma(M(12), M(1))    =     M3124 + M3142 + 2M4132.
sigma(M(111), M(1))    =     -M2134-2M2143 -M2413-M3142 + M3214.
Cocycles of total degree 5
sigma(M(1), M(4))    =     2M21345 + M23145 + M31245 + M23415 + M41235.
sigma(M(1), M(31))    =     -2M21345-4M21354 -M23145-M31245 + M13452-2M21453 -2M21534-2M23154
-2M31254-M23514 -M24153-2M25134 -M31452-M31524 -M41253-M25314
-M35124-M41352 -2M52134-M52314 -M53124.
sigma(M(1), M(22))    =     -2M21345-4M21435 -2M21453-2M21534 -2M24135-2M31425 + M14523-2M24153
-2M31524-2M32415 -2M42135-M24513 -2M32514-M41523 -2M42153-3M42513.
sigma(M(1), M(13))    =     M15234 + M25134 + M35124 + 2M52134 + M52314 + M53124.
sigma(M(1), M(211))    =     2M21345-M13425 + 2M21354 + 4M21435 -M13452-M13524 + 4M21453 + 4M21534
+ 2M24135 + M31425 -2M13542-M14523 + 6M21543 + 2M24153 + 2M25134 + M31452
+ M31524 + 2M42135 -M14532-M15342 + 2M24513 + 4M25143 + 2M31542 + M41523
+ 2M42153 + 2M52134 + 2M25413 + M35142 + M41532 + 2M42513 -M51342 + 4M52143
+ M45132 + 2M45213 + 2M52413 + M53142 + 2M54213.
sigma(M(1), M(121))    =     -M14235-M14253 -M15234-M24135 -M14523-2M15243 -M24153-M25134
-2M42135-2M15423 -M24513-2M25143 -2M42153-2M52134 -2M25413-M35142
-2M42513 + M51342 -M51423-4M52143 -2M45213-3M52413 -M53142-4M54213.
sigma(M(1), M(112))    =     -M13245-M13425 -M14235-M13452 -3M14325-M15234 -2M14352-2M15324
-M24315-M41325 -M14532-M15342 -M25314-M41352 -M41532 + M51423
-M45132 + M52413 + 2M54213.
sigma(M(1), M(1111))    =     M13245 + M13254 + M13425 + M14235 + M13452 + M13524 + M14253 + 2M14325
+ M15234 + M13542 + 2M14352 + M14523 + M15243 + 2M15324 + 2M14532 + 2M15342
+ 2M15423 + 3M15432.
sigma(M(2), M(3))    =     2M13245 + M13425 + M14235 + M23145 + M31245 + M13452 + M15234 + M24135
+ M31425 + M25134 + M31452 + 2M34125 + M34152 + M35124.
sigma(M(2), M(21))    =     -2M13245 + M12453 -4M13254-M13425 -M14235-M23145 -M31245-3M13524
-2M14253-M15234 -2M23154-M24135 -2M31254-M31425 -2M13542-M14523
-2M15243-2M15324 -M23514-2M24153 -M25134-M31452 -2M31524-M15342
-2M15423-M24513 -2M25143-M25314 -2M31542-M34152 -M35124-2M51324
-2M25413-2M35142 -M51342-M51423 -M52314-M53124 + 2M45132-M52413
-M53142.
sigma(M(2), M(12))    =     -2M13245 + M12534 -2M13425-2M14235 -2M13452 + M13524 -6M14325-M15234
-4M14352 + M14523 -2M15324 + M23514 -2M24315-2M41325 -2M14532-M15342
+ M24513-M25314 -2M41352 + 2M51324 -2M41532 + M51342 + M51423 + M52314
+ M53124-2M45132 + M52413 + M53142.
sigma(M(2), M(111))    =     -M12435 + 2M13245 -M12453-M12534 + 2M13254 + M13425 + M14235-2M12543
+ M13452 + M13524 + M14253 + 3M14325 + M15234 + 3M14352 + 3M15324 + 2M14532
+ 2M15342 + 2M15423 + 4M15432.
sigma(M(11), M(3))    =     -M21345-4M21354 -2M21453-2M21534 -2M23154 + M23415 -2M31254 + 3M32145
+ M41235-M23514 -M24153-2M25134 -2M31452-M31524 + 2M32415-M41253
+ 2M42135-M25314 -M34152 + M34215 -M35124-M41352 + M42315 + M43125.
sigma(M(11), M(21))    =     M21345-M13425 + 2M21354 + 4M21435 -M23145-M31245 -M13452-M13524
+ 6M21453 + 5M21534 -2M23154 + 2M24135 -2M31254 + M31425 -3M32145-2M13542
-M14523 + 12M21543 -M23514 + 2M24153 + 3M25134 + 3M31452 -6M32154-2M32415
-M41253-2M14532 -M15342 + 3M24513 + 8M25143-M25314 + 6M31542-5M32514
-M35124 + M41523 -2M42153 + M52134 + 4M25413 + 3M35142 -3M35214 + 2M41532
-M42513-M43152 + 4M52143-M52314 -M53124 + M45213 + 2M52413 + 2M53142
-3M53214.
sigma(M(11), M(12))    =     -M21345-M14235 -2M21435-M14253 -M15234-M21453 -2M24135-M31425
-M14523-2M15243 -2M24153-M32415 -3M42135-M15342 -2M15423-2M24513
-2M25143 + M25314 + M35124-3M42153 -M52134-2M25413 -M35142 + 2M35214
-3M42513-4M52143 + M52314 + M53124 -M45213-2M52413 -2M53142 + 3M53214.
sigma(M(11), M(111))    =     M13245 + M21345 + 2M13254 + M13425 + M14235 + M21354 + M21435 + M13452
+ 2M13524 + 2M14253 + 2M14325 + M15234 + M21453 + M21534 + 2M13542 + 3M14352
+ 2M14523 + 2M15243 + 3M15324 + M21543 -M24315-M41325 + 4M14532 + 4M15342
+ 4M15423-M25314 -M41352 + 8M15432 -M25413-M41532.
sigma(M(3), M(2))    =     2M12435 + M12453 + M12534 + M13425 + M14235 + M13524 + M14253 + M23415
+ M41235 + 2M14523 + M23514 + M41253 + M24513 + M41523.
sigma(M(3), M(11))    =     M12354-2M12435 -M12453-M12534 -M13425-M14235 -3M12543-M13524
-M14253-2M13542 -2M14523-2M15243 -M14532-M15342 -M15423.
sigma(M(21), M(2))    =     -2M13245-4M13254 -M13425-M14235 -M31245-M13452 -3M13524-3M14253
-M15234-2M23154 + M23415-2M31254 -M31425-2M13542 -2M14352-2M14523
-2M15243-2M15324 -M23514-2M24153 + 2M24315-M31452 -2M31524 + M34125
-M41253-2M14532 -2M15342-2M15423 -M24513-2M25143 -2M31542-M34152
+ 2M34215-M41352 -M41523 + M42315 -2M51324-2M25413 -2M35142 + 2M35214
-2M41532-M51342 -M51423-M52314 -M53124 + 2M45213 -M52413-M53142.
sigma(M(21), M(11))    =     -M12435 + 2M13245 -M12453-M12534 + 4M13254 + M13425 + M14235-M23145
-3M12543 + M13452 + 3M13524 + 3M14253 + 3M14325 + M15234 -M23154-M24135
+ M13542 + 5M14352 + 2M14523 + M15243 + 5M15324-M24153 -2M24315-M25134
+ 5M14532 + 5M15342 + 5M15423-M25143 -2M25314-M51243 + 2M51324 + 12M15432
-2M25413 + M51342 + M51423 + M45132 + 3M51432.
sigma(M(12), M(2))    =     -2M21345-4M21435 + M31245-2M21453 -2M21534-2M24135 -M31425 + M41235
-2M24153 + M31452 -2M31524-2M32415 + M34125 + 2M41325 -2M42135-2M24513
-2M32514 + M34152 + M41352-2M41523 -2M42153 + M42315 + 2M43125 + 2M51324
-4M42513 + 2M43152 + M51342 + M51423 + M52314 + M53124 -2M45213 + M52413
+ M53142.
sigma(M(12), M(11))    =     -M13245-M13425 -M14235-M31245 -M13452-3M14325 -M15234-M31254
-M31425-2M14352 -2M15324-M24315 -M31452-M31524 -3M41325-M14532
-M15342-M15423 -M25314-M31542 -3M41352 + M51243 -2M51324-M25413
-3M41532-M51342 -M51423-M45132 -3M51432.
sigma(M(111), M(2))    =     M21345 + 4M21435 -M23145-M31245 + 3M21453 + 3M21534 -2M23154 + 2M24135
-2M31254 + 2M31425 -2M32145 + 6M21543 -M23514 + M24153 + M25134 + M31452
+ M31524-6M32154 + M32415-M41253 + M42135 + 2M24513 + 4M25143-M25314
+ 4M31542-3M32514 -M34152 + M34215 -M35124-M41352 + 2M41523-3M42153
+ M42315 + M43125 + 2M25413 + 2M35142 -3M35214 + 2M41532 -3M43152 + 4M43215.
sigma(M(111), M(11))    =     M13245 + M21345 + M13254 + M13425 + M14235 + 2M21354 + M21435 + M13452
+ M13524 + M14253 + 3M14325 + M15234 + 2M21453 + 2M21534 -M32145 + M13542
+ 3M14352 + M14523 + M15243 + 3M15324 + 3M21543 + M25134 + M31452-M32154
-M32415-M42135 + 3M14532 + 3M15342 + 3M15423 + M25143 + M31542-M32514
-M42153 + 6M15432 -M42513.
sigma(M(4), M(1))    =     2M12354 + M12453 + M12534 + M13452 + M15234.
sigma(M(31), M(1))    =     -2M12435-2M12453 -2M12534-M13425 -M14235-6M12543 -M13452-M13524
-M14253-M15234 + M23415-4M13542 -2M14523-4M15243 + M23514-2M14532
-2M15342-2M15423 + M24513-2M51243 -M51342-M51423.
sigma(M(22), M(1))    =     -2M13245-2M13425 -2M14235-2M13452 -6M14325-2M15234 -4M14352-4M15324
-2M24315 + M34125 -2M41325-2M14532 -2M15342-2M15423 -2M25314 + M34152
+ M35124-2M41352 -2M25413 + M35142 -2M41532.
sigma(M(13), M(1))    =     M41235 + M41253 + M41523 + 2M51243 + M51342 + M51423.
sigma(M(211), M(1))    =     2M13245 + 2M13254 + 2M13425 + 2M14235 -M23145 + 2M13452 + 2M13524 + 2M14253
+ 6M14325 + 2M15234 -2M23154-M24135 + 2M13542 + 6M14352 + 2M14523 + 2M15243
+ 6M15324-M23514 -2M24153-M25134 + 2M41325 + 6M14532 + 6M15342 + 6M15423
-M24513-2M25143 -M25314-M34152 + M34215 + 2M41352 + 2M51324 + 12M15432
-2M25413-M35142 + M35214 + 2M41532 + 2M51342 + 2M51423 -M52314 + 2M45132
+ M45213 + 6M51432 -M52413 + 2M54132.
sigma(M(121), M(1))    =     -M31245-2M31254 -M31425-M31452 -2M31524-M41253 -2M41325-2M31542
-M35124-3M41352 -M41523 + M42315 -2M51324-M35142 -4M41532-2M51342
-2M51423 + M52314 -M53124-2M45132 -6M51432 + M52413 -M53142-4M54132.
sigma(M(112), M(1))    =     -M21345-2M21435 -M21453-M21534 -M24135-M31425 -M24153-M31524
-M32415-M42135 -M24513-M32514 -M41523-M42153 + M43125-2M42513
+ M43152 + M53124 -M45213 + M53142 + 2M54132.
sigma(M(1111), M(1))    =     M21345 + M21354 + 2M21435 + 2M21453 + 2M21534 + M24135 + M31425-M32145
+ 3M21543 + M24153 + M25134 + M31452 + M31524-2M32154 + M24513 + 2M25143
+ 2M31542-M32514 + M41523-M42153 + M25413 + M35142 -M35214 + M41532
-M43152 + M43215.
Cocycles of total degree 6
sigma(M(1), M(5))    =     2M213456 + M231456 + M312456 + M234156 + M412356 + M234516 + M512346.
sigma(M(1), M(41))    =     -2M213456-4M213465 -M231456-M312456 -2M213564-2M213645 -2M231465-M234156
-2M312465-M412356 + M134562-2M214563 -2M216345-M231564 -M231645-2M234165
-M312564-M312645 -2M412365-M234615 -M235164-M236145 -M241563-2M261345
-M314562-M316245 -M412563-M412635 -M512364-M236415 -M245163-M263145
-M361245-M413562 -M416235-M512463 -2M621345-M263415 -M461235-M513462
-M623145-M631245 -M623415-M641235.
sigma(M(1), M(32))    =     -2M213456-4M213546 -M231456-M312456 -2M213564-2M213645 -2M214536-2M215346
-2M231546-2M312546 -2M214635-2M215364 -M231564-M231645 -M235146-M241536
-2M251346-M312564 -M312645-2M314526 -M315246-M412536 -4M215634-M235164
-M241635-2M251364 -M253146-2M314625 -M315264-2M324516 -M341526-M351246
-M412635-M413526 -2M521346 + M145623 -M235614-3M251634 -M253164-3M315624
-2M324615-M341625 -M342516-M351264 -M413625-M423516 -M512634-2M521364
-M523146-M531246 + M245613-M253614 -2M256134-2M325614 -M342615-2M351624
-M415623-M423615 -M513624-2M521634 -M523164-M531264 -M256314-M352614
-M356124-M425613 -M514623-2M523614 -2M526134-M531624 -M524613-M526314
-M536124-2M562134 + 2M456213-M562314 -M563124.
sigma(M(1), M(23))    =     -2M213456-4M214356 -2M214536-2M215346 -2M241356-2M314256 -2M214563-2M216345
-2M241536-2M315246 -2M324156-2M421356 -2M241563-2M245136 -2M316245-2M325146
-2M415236-2M421536 + M156234-2M245163 -2M326145-2M416235 -2M421563-4M425136
-2M245613 + M256134 -2M425163-2M426135 -2M435126-2M452136 -M516234 + M356124
-2M425613-2M436125 -2M452163-M526134 -2M452613-M536124 + 2M562134-2M456213
+ M562314 + M563124.
sigma(M(1), M(14))    =     M162345 + M261345 + M361245 + 2M621345 + M461235 + M623145 + M631245 + M623415
+ M641235.
sigma(M(1), M(311))    = The Code Crashed here due to MAPLE's sorting code
   
Created 5 August 2002