1620 Permutations, etc. 



Partitions, continued. 



7-, of X. Xirkman, T. P. Manch. Ph. S. Mm. 



14 (1857) 137-. 

 self -opposite, number of. Durfee, W. P. (xn) 



[1882J J. H. Un. Cir. [2] (1883) 23. 

 , (Durfee). Sylvester, J. J. (xn) 



J. H. Un. Cir. [2] (1883) 23-, 42-. 

 theorem. Glaisher, J. W. L. [1879-83] Mess. 



Mth. 9 (1880) 47-; 12 (1883) 158-. 

 . Sylvester, J. J. C. E. 96 (1883) 674^. 

 , new. Sylvester, J. J. (xn) J. H. Un. 



Cir. [2] (1883) 70. 

 theorems. Mansion, P. Mess. Mth. 5 (1876) 



90. 

 . Glaisher, J. W. L. Mess. Mth. 5 (1876) 



91. 

 theory, note. Sylvester, J. J. B. A. Ep. 41 



(1871) (Sect.) 23-. 



Perfect partitions of numbers and compositions 

 of multipartite numbers. Macmahon, (Major) 

 P. A. Mess. Mth. 20 (1891) 103-. 



Permutants, theory. Cayley, A. Camb. and 

 Dubl. Mth. J. 7 (1852) 40-, 97-. 



Permutation, alternate, probability of. Andre, 

 D. C. E. 97 (1883) 983-. 



, geometrical. Cayley, A. Ph. Mg. 30 

 (1865) 370-. 



numbers, approximate calculation. Schlo- 

 rnilch, 0. Z. Mth. Ps. 10 (1865) 232-. 



PEEMUTATIONS. 



Conti, C. Padova N. Sag. 3 (1831) 90-. 

 Cayley, A. Ph. Mg. 34 (1849) 527-. 

 Bourget, J. N. A. Mth. 10 (1871) 254-. 

 Lucas, E. As. Fr. C. E. (1883) 83-. 

 alternate. Andre, D. Liouv. J. Mth. 7 (1881) 

 167-. 



and quasi-alternate, relation between num- 

 ber of. Andre, D. Par. S. Phlm. Bll. 8 

 (1896) 5-. 



application of new method to. Sprague, T. B. 



Edinb. E. S. T. 37 (1895) 399-. 

 a certain species. Andre, D. Par. S. Phlm. 



Mm. Cent. (1888) 35-. 

 circular, applications to theory of numbers. 



MacMahon, (Maj.) P. A. L. Mth. S. P. 23 



(1892) 305-. 



distinct. Moreau, C. N. A. Mth. 11 (1872) 

 309-. 



, notion of maxima and minima in. Andre, 



D. Par. S. Phlm. Bll. 5 (1893) (C. E. No. 11) 



2-. 

 , sequences. Andre, D. Par. S. Mth. Bll. 



23 (1895) 122-. 

 and combinations. Pagnini, G. M. Brugna- 



telli G. 3 (1810) 329-. 

 . Warburton, H. [1847] Camb. Ph. S. 



T. 8 (1849) 471-. 

 . Whitworth, W. A. [1865] Mess. Mth. 



3 (1866) 193-. 

 , problem. Balbo, P. Turin Mm. Ac. 14 



(1804-5) 224-. 



Permutations 1620 



and combinations, proofs of theorems, and of 

 theorem in stereometry. Seidelin, C. J. L. 

 (xn) Ts. Mth. 6 (1870) 20-, 22-; 6 (1876) 

 63-. 



, theory. Hertzsprung, S. (xn) Ts. 

 Mth. 5 (1869) 97-. 



continuous, by uniform law. Paradisi, G. 

 [1816] Mod. Mm. S. It. 18 (1818) 143-. 



and cyclic arrangements, theory. Jablonski, E. 

 C. E. 114 (1892) 904- ; Liouv. J. Mth. 8 

 (1892) 331- ; Prace Mt.-Fiz. 4 (1893) 



of first n integers, method of deducing con- 

 secutively. Renshaw, A. Mess. Mth. 4 

 (1868) 36-. 



numbers, distribution into 4 groups. 



Andre, D. Par. S. Phlm. Bll. 5 (1893) 

 33-. 



n letters, classification in groups. Despeyrous, 

 C. Liouv. J. Mth. 10 (1865) 177-. 



2q letters alike in pairs. Vachette, A. N. 

 A. Mth. 13 (1874) 549-; 14 (1875) 299-, 

 337-. 



3q letters alike in threes. Vachette, A. N. 

 A. Mth. 14 (1875) 438-. 



. Moreau, C. N. A. Mth. 15 



(1876) 90-. 

 . Vachette, A. N. A. Mth. 15 



(1876) 114-, 145-, 193-. 

 limited. Laisant, C. A. C. E. 112 (1891) 



1047-. 

 maxima, minima and sequences. Andre, D. 



Par. EC. Norm. A. 1 (1884) 121-. 

 new calculus, applicable to theory. Cauchy, 



A. L. C. E. 22 (1846) 53-, 99-. 



demonstration of theorem. Andre, D. Par. 

 S. Phlm. Bll. 3 (1891) 153-. 



notes. Morley, F. N. Y. Mth. S. Bll. 3 (1894) 



142-. 

 of a number, sum. Marre, A. N. A. Mth. 5 



(1846) 57-. 



n objects. Bourget, J. N. A. Mth. 2 (1883) 

 433-. 



problem. Barlow, P. Nicholson J. 23 (1809) 



203-. 

 . Arndt, F. Grunert Arch. 3 (1843) 



210-. 

 . Allardice, R. E. Edinb. Mth. S. P. 8 



(1890) 64-. 



. Lagrandval, de. Bordeaux S. Sc. PV. 



(1895-96) 22-. 

 , solution. Drot, . N. A. Mth. 5 (1846) 



97-. 

 problems, two. Laisant, . Par. S. Mth. Bll. 



19 (1891) 105-. 

 quasi-alternate. Andre, D. C. E. 119 (1894) 



947-; Liouv. J. Mth. 1 (1895) 315-. 

 with restrictions as to placing. Kantor, S. 



Z. Mth. Ps. 28 (1883) 379-. 

 Schubert's solution of Bachet's problem. 



Busche, E. Mth. A. 47 (1896) 105-. 

 self -con jugate. Muir, T. Edinb. E. S. P. 17 



(1891) 7-. 



. MacMahon, (Maj.) P. A. Mess. Mth. 24 



(1895) 69-. 

 with sequences. Morley, F. [1897] N. Y. Am. 



Mth. S. Bll. 4 (1898) 23-. 



