2410 Symmetric Functions 



new theory. MacMahon, P. A. Am. J. Mth. 

 11 (1889) 1- ; 12 (1890) 61- ; 13 (1891) 193- ; 



14 (1892) 15-. 



Newton's propositions, proof. Steen, A. Ts. 

 Mth. 3 (1885) 30-; Fschr. Mth. (1885) 111. 



theorem. Tweedie, C. Edinb. Mth. S. P. 

 11 (1893) 61. 



operators. Lachlan, B. L. Mth. S. P. 18 



(1886-87) 39- ; 19 (1889) 294-. 

 of pairs of variables. Brill, A. Gott. Nr. 



(1893) 757-. 

 partition problem. Lemoyne, G. G. Mt. 10 



(1872) 93-. 

 problem. Holmboe, B. M. Mg. Ntvd. 2 (1836) 



279-. 

 properties of a complete table. MacMahon, 



P. A. Am. J. Mth. 10 (1888) 42-. 

 rational, calculation with. Hoppe,R. Schlomilch 



Z. 4 (1859) 353-. 

 relation between forms. Kostka, C. [1881] 



Crelle J. Mth. 93 (1882) 89-. 



, and invariants. Gambioli, D. G. Mt. 

 29 (1891) 41-. 



representation by sums of powers. Hankel, H. 



[1865] Crelle J. 67 (1867) 90-. 

 of roots and combinations of coefficients of 



weight 11 and 12. Rehofovsky, W. [1882] 



Wien Ak. D. 46 (1883) (Ab. 2) 53-. 

 common to several equations. Betti, E. 



Tortolini A. 1 (1858) 193-. 

 2 equations. Dewulf, . N. A. 



Mth. 19 (I860) 18-. 

 2 equations, representation. Hess, E. 



Z. Mth. Ps. 15 (1870) 325-. 

 of a pair of cubic equations. Walker, J. J. 



[1865] Mess. Mth. 3 (1866) 107-. 

 and resultants of simultaneous equations. 



Escherich, G. von. Wien Ak. D. 36 (1876) 



(Ab. 2) 251-. 

 of systems of equations. MacMahon, P. A. 



[1890] Phil. Trans. (A) 181 (1891) 481-. 

 2 equations. Cayley, A. Phil. 



Trans. (1857) 717-. 

 , tables to the degree 10. Cayley, A. 



Am. J. Mth. 7 (1885) 47-. 

 satisfying partial differential equations. Netto, 



E. Z. Mth. Ps. 38 (1893) 357-. 

 and seminvariants. Cayley, A. Am. J. Mth. 



15 (1893) 1-. 



of several series of variables. Junker, F. Mth. 



A. 43 (1893) 225-. 

 simple and complete, relation. Crocchi, L. 



[1879] G. Mt. 18 (1880) 377-. 



of sines of angles ( a -\ ] . Johnson, W. W. 



Des Moines Anal. 6 (1879) 105-. 



specified number of roots. Murphy, E. (vi 

 Adds.) Ph. Mg. 10 (1831) 413-. 



symbolical representation and invariant charac- 

 ters. Gambioli, D. G. Mt. 30 (1892) 

 192-. 



tabulation. Durfee, W. P. Am. J. Mth. 5 

 (1882) 348-. 



in terms of coefficients. Mainardi, G. Em. 

 At. N. Line. 20 (1867) 163-. 



theorem. Cockle, Jas. Ph. Mg. 28 (1846) 

 132-. 



Symmetric Functions 2420 



theorem of Cauchy. Bertrand, J. C. B. 45 



(1857) 1-. 

 theorems. Analin, A. H. H. [1880-83] Ir. 



Ac. P. 3 (1883) 289-; Edinb. K. S. P. 12 



(1884) 236-. 

 theory. Schonemann, T. Crelle J. 19 (1839) 



231-, 289-. 

 . Cockle, Jas. Mathematician 3 (1850) 



176-, 246-; Suppl. 27-. 

 . Borchardt, C. W. Berl. B. (1855) 165-. 

 . Mertens, F. Crelle J. 69 (1868) 289-; 



Wien Ak. Sb. 81 (1880) (Ab. 2) 988-. 

 . Anglin, A. H. Crelle J. Mth. 98 (1885) 



175-. 

 . Konig, G. Mth. Termt. Ets. 8 (1890) 9-; 



Mth. Nt. B. Ung. 8 (1891) 83-. 

 . Mertens, F. Wien Ak. Sb. 108 (1899) 



(Ab. 2a) 473-. 

 and theory of distributions. MacMahon, P. A. 



L. Mth. S. P. 19 (1889) 220-. 

 of 12 ic , tables. Durfee, W. P. Am. J. Mth. 



5 (1882) 45-. 



13 ic . MacMahon, P. A. Am. J. Mth. 6 

 (1884) 289-. 



14 ic . Durfee, W. P. Am. J. Mth. 9 (1887) 

 278-. 



two ternary forms. Junker, F. Wien Ak. 

 D. 64 (1897) 439-. 



Waring's formula. MacMahon, P. A. Mess. 

 Mth. 14 (1885) 8-. 



formulae. Terquem, 0. N. A. Mth. 8 (1849) 

 76-. 



Vieille, J. C. B. 44 (1857) 1311-. 

 ,. . . and differentials of sums of kth 



powers of roots. Serret, J. A. C. B. 45 

 (1857) 60-. 



Symmetry of a certain algebraic expression, 

 proof. Allardice, R. E. Edinb. Mth. S. P. 

 4 (1886) 37. 



, law. MacMahon, P. A. QJ. Mth. 22 (1887) 



Teleological method. Dickstein, S. Prace 



Mt.-Fiz. 3 (1892) 126- ; Fschr. Mth. (1892) 



97-. 

 ', Wronski's. Krauze, W. Prace Mt.-Fiz. 



3 (1892) 110- ; Fschr. Mth. (1892) 97. 

 Wronski's formulae, proof of two. Dickstein, S. 



Krk. Ak. (Mt.-Prz.) Pam. 12 (1886) (87)-; 



Fschr. Mth. (1886) 121. 



2420 Reality, multiplicity, 

 separation, of roots. 



Algebra, fundamental theorem and Newton's 



approximation method. Mertens, F. Wien 



Ak. Sb. 101 (1892) (Ab. 2a) 415-. 

 Algebraic equations and Campbell's quadratic 



functions. Poulain, A. C. B. 106 (1888) 



470-, 562, 1479. 

 , general theorems. Poulain, A. N. A. 



Mth. 6 (1867) 21-. 



163 



L2 



