Permutations, continued. 



square, of base 6. Tarry, G. Liege S. Sc. 



Mm. 2 (1900) No. 1, 10 pp. 

 successive, problem of Monge's. Bourget, J. 



Liouv. J. Mth. 8 (1882) 413-. 

 theorem of MacMahon's. Gegetibauer, L. Mb.. 



Mth. Ps. 11 (1900) 287-. 

 theory. Despeyrous, C. Liouv. J. Mth. 6 



(1861) 417-. 

 transformation and classification. Sprague, 



T. B. Edinb. Mth. S. P. 9 (1891) 59-. 



1620 Permutations, Combinations, Partitions, Distributions, etc. 1620 



Sum of numbers of all variations p + 1, p + 2 . . . 

 to ?d;h class inclusive =n (n- 1) ... (n-p- 1) 

 {[e(n-p) !]-!} Huber,M.T. Wiad. Mt. 

 3 (1899) 39-; 4 (1900) 93; Fschr. Mth. 

 (1899) 208. 



Symmetric functions of numbers, and their 

 partition. Scott, G. [1865] QJ. Mth. 7 

 (1866) 81-. 



Tactic disclosing existence of 4-valued func- 

 tions. Sylvester, J. J. Ph. Mg. 21 (1861) 

 515- ; 22 (1861) 45-. 

 of 9 elements. Sylvester, J. J. Ph. Mg. 22 



(1861) 144-. 

 Tactical memoranda. Moore, E. H. Am. J. 



Mth. 18 (1896) 265-. 

 Ternary systems of 13 elements. Pasquale, V. 



de. Mil. I. Lomb. Ed. 32 (1899) 213-. 

 Thirty cubes constructed with six differently 

 coloured squares. MacMahon, (Maj.) P. A. 

 L. Mth. S. P. 24 (1893) 145-. 

 Thirty-six officers, problem. Tarry, G. As. 



Fr. C. K. (1900) (Ft. 2) 170-. 

 'Trees.' Cayley,A. Ph. Mg. 13 (1857) 172- ; 



18 (1859) 374-. 

 . Polignac, C. de. Par. S. Mth. Bll. 8 



(1880) 120- ; 9 (1881) 30-. 

 . Cayley, A. (xn) J. H. Un. Cir. [1] 



(1882) 202. 

 . Sylvester, J. J. (xn) J. H. Un. Cir. [1] 



(1882) 202-. 



, with application to theory of chemical com- 

 binations. Cayley, A. B. A. Ep. (1875) 

 257-; Am. J. Mth. 4 (1881) 266-. 



, . Delannoy, H. As. 



Fr. C. E. (1894) (Pt. 2) 102-. 

 , isomers, theory. Cayley, A. Ph. Mg. 47 



(1874) 444-. 

 , number of univalent radicals C,,!!^,,. 



Cayley, A. [1876] Ph. Mg. 3 (1877) 34-. 

 , theorem. Cayley, A. QJ. Mth. 23 (1889) 



376. 



, yoke-chains and multipartite compositions 

 in connexion with. MacMahon, (Maj.) P. A. 

 L. Mth. S. P. 22 (1891) 330-. 

 Triads. Fifteen girl problem. Kirkman, T. P. 

 Ph. Mg. 37 (1850) 169; 23 (1862) 199-. 



. (Kirkman). Woolhouse, W. S. B. 



Ph. Mg. 22 (1861) 510- . 



. . Cayley, A. Ph. Mg. 25 (1863) 59-. 



. . Power, J. [1865] QJ. Mth. 8 



(1867) 236-. 



. . Frost, A. H. QJ. Mth. 11 



(1871) 26-. 



. . Johnson, W. W. Am. J. Mth. 



2 (1879) 397-. 



. . Story, W. E. Am. J. Mth. 2 



(1879) 399-. 

 . . Mertelsmann, A. F. H. Z. 



Mth. Ps. 43 (1898) 329-. 

 . , cyclic solution. Peirce, B. 

 Gould As. J. 6 (1861) 169-. 



. , geometric picture of. Davis, 



E. W. A. Mth. 11 (1896-97) 156-. 



. ,3 methods and 48 solutions. 



Frazer, P. (jun,). Am. Ph. S. P. 18 (1880) 

 505-. 



. , note on theory. Tait, P. G. 



Edinb. E. S. P. 10 (1880) 664-. 



Polygons, division into triangles. (Segner's 



numbers.) Lame, G. Liouv. J. Mth. 3 



(1838) 505-. 

 , . ( .) Tellkampf, A. Grunert 



Arch. 2 (1842) 117-. 

 , . ( .) Catalan, E. C. 



[1870] Liege S. Sc. Mm. 13 (1886) 54-, 



399. 

 , . ( .) Rowe, E. C., & Taylor, 



H. M. L. Mth. S. P. 13 (1881-82) 102-. 

 , . ( .) Gelin, (I'abbe) E. (xn) 



Mathesis 3 (1883) 108-. 

 , . ( .) Catalan, E. C. [1886] 



Palermo Cir. Mt. Ed. 1 (1887) 190-. 

 Polynomial coefficients. Piuma, C. M. G. Mt. 



29 (1891) 34-. 

 . Klekler, P. Mh. Mth. Ps. 10 (1899) 



218-. 

 , properties. Sadun, E. G. Mt. 31 (1893) 



119-, 379. 

 theorem. Ladd, C. Des Moines Anal. 5 



(1878) 145-. 

 Products of n factors, number of. Eodrigues, 0. 



Liouv. J. Mth. 3 (1838) 549. 

 Quadricycles of 8;i + l elements, construction. 



Brunei, G. Bordeaux S. Sc. PV. (1895-96) 



58-. 



n elements, systems. Brunei, G. Bor- 

 deaux S. Sc. PV. (1898-99) 59-. 

 " Quotites " of combinations. Soule, . Bor- 

 deaux S. Sc. Mm. 3 (1893) xiv-, xxv-. 

 Series for n ! . Heather, J. F. Mathematician 



2 (1847) 296-. 



properties and application. Unferdinger, F. 

 Wien Sb. 67 j(1873) (Ab. 2) 363-. 



7l w 



2 : for -i = l,2, 3, 4, 5, summation. Dobin- 



ski, G. Arch. Mth. Ps. 61 (1877) 333-. 

 Signs, successions of, and application to 



coloured tiles and Newton's rule, etc. 



Sylvester, J. J. Ph. Mg. 34 (1867) 461-. 

 Stifel's bordered squares. Fontes, . As. Fr. 



C. E. (1895) (Pt. 2) 248-. 

 Sub-factorial N. Whitworth, W. A. Mess. 



Mth. 7 (1878) 145-. 

 Sum of the cubes of the coefficients in (1 - z) 2 ". 



Richmond, H. W. Mess. Mth. 21 (1892) 



77-. 



