A Theorem on Rational Integral Symmetric Functions

John Dougall
1929 Mathematical Notes  
An identity involving symmetric functions of n letters may in ĉ ertain class of cases be extended immediately to a greater number of letters. For example, the theorem (a + b) 2 = a 2 + *> 2 + 2ab may be written (2 a) 2 = 2a 2 + 2 2a6; and in the latter form it is true for any number of letters. Similarly with the theorem (a + b + c) 3 = a 3 + b 3 + c 3 + 3a 2 (b + c) + 36 2 (c + a) + 3c 2 (a + b) + 6a6c; (1) in the form it is true for any number of letters. The symmetric functions which occur
more » ... tions which occur in these results, such a» 2 a 3 , 2 a* 6, Habc are monomial symmetric functions, being of the form 2 aP b'i c r
doi:10.1017/s1757748900001894 fatcat:xi7n65hkm5gsjd5dy6tt4lnw6a