Elements of the Monomial Basis of SSym in Terms of the Fundamental Basis

Monomial Functions for permutations in S2
M12 = F12-F21.
M21 = F21.
Monomial Functions for permutations in S3
M123 = F123-F132 -F213 + F321.
M132 = F132-F231.
M213 = F213-F312.
M231 = F231-F321.
M312 = F312-F321.
M321 = F321.
Monomial Functions for permutations in S4
M1234 = F1234-F1243 -F1324-F2134 + F2143 + F1432 + F3214-F4321.
M1243 = F1243-F1342 -F2143 + F3241.
M1324 = F1324-F1423 -F2314 + F2413.
M1342 = F1342-F1432 -F2341 + F2431.
M1423 = F1423-F1432 -F2413 + F3421.
M1432 = F1432-F2431.
M2134 = F2134-F2143 -F3124 + F4132.
M2143 = F2143-F3142.
M2314 = F2314-F2413 -F3214 + F4312.
M2341 = F2341-F2431 -F3241 + F4321.
M2413 = F2413-F3412.
M2431 = F2431-F3421.
M3124 = F3124-F3214 -F4123 + F4213.
M3142 = F3142-F3241 -F4132 + F4231.
M3214 = F3214-F4213.
M3241 = F3241-F4231.
M3412 = F3412-F3421 -F4312 + F4321.
M3421 = F3421-F4321.
M4123 = F4123-F4132 -F4213 + F4321.
M4132 = F4132-F4231.
M4213 = F4213-F4312.
M4231 = F4231-F4321.
M4312 = F4312-F4321.
M4321 = F4321.
Created 4 August 2002