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



Enumeration of groups of totitives. Tanner, 

 H. W. L. L. Mth. S. P. 27 (1896) 329-. 



Equations, linear, symbolic, solution in con- 

 nection with theory of permutations. 

 Cauchy, A. L. C. B. 21 (1845) 1123-. 



Factorial functions. Piani,D. [1847] Bologna 

 Mm. Ac. Sc. 1 (1850) 511-. 



numeration applied to permutations. Lais- 

 ant, C. A. Par. S. Mth. Bll. 16 (1888) 

 176-. 



n\fr\ (n-r)\ an integer. Miller, W. H. 

 Crelle J. 13 (1835) 257-. 



m(m + l)...(m + n-l). Liouville,J. Liouv. 

 J. Mth. 2 (1857) 277-. 



Factorials. Bellavitis, G. A. Sc. Lomb. 



Yen. 4 (1834) 10-. 



. McCulloch, J. F. A. Mth. 4 (1888) 

 . 161-. 

 , approximate expression for xl Forsyth, 



A. E. B. A. Bp. (1883) 407-. 

 , value of n! Liouville, J. Liouv. J. 



Mth. 4 (1839) 317-. 

 , when n is large. Serret, J. A. 



C. B. 50 (1860) 662-. 



(faculties). Oettinger, L. Crelle J. 33 

 (1846) 1-, 117-, 226-, 329-; 35 (1847) 13-; 

 38 (1849) 162-, 216- ; 44 (1852) 26-, 147-. 



and faculties, treatment by limits. Ohm, H. 

 Crelle J. 39 (1850) 23-. 



, W. G. Homer's method. Homer, J. [1872] 



QJ. Mth. 12(1873)258-. 

 , new method. Nicholson, P. Tilloch Ph. 



Mg. 53 (1819) 412-. 

 , theorem. Andre, D. (ix) Par. S. 



Mth. Bll. 1 (1873) 84-. 

 , numerical values. Kotel'nikov, P. I. (xn) 



Kazan Un. Mm. ((1848) Bk. 4) 9-. 

 , ratios of reciprocal. Cauchy, A. L. C. B. 



17 (1843) 921-, 1159-. 

 , theorem. Gomes Teixeira, E. Arch. Mth. 



Ps. 2 (1885) 265-. 

 Faculties, geometric, and transformation of 



logs, into definite integrals. Cauchy, A. L. 



C. B. 17 (1843) 779-. 



and powers ; analogy. Ampere, A.M. Ger- 

 gonne A. Mth. 15 (1824-25) 369-. 



, quotients of two. Schlomilch, 0. Schlo- 



milch Z. 3 (1858) 322-. 

 , remarks on some. Guibert, M. P. A. N. 



A. Mth. 19 (1860) 213-. 

 , theorem. Schlomilch, 0. Grunert Arch. 



7 (1846) 331-. 

 , theory. Bessel, F. W. Konigsb. Arch. 1 



(1812) 241-.' 

 , . Kramp, C. Gergonne A. Mth. 3 (1812- 



13) 1-, 114-, 325-. 

 , . Miiller, A. Crelle J. 11 (1834) 



361-. 

 Faculty coefficients. Studnicka, F. J. Prag 



Ceske Ak. Fr. Jos. Bz. (Trida 2) 9 (1900) 



Art. 17, 10pp.; Fschr. Mth. (1900) 156-. 

 , determination. Schlomilch, 0. Grunert 



Arch. (1848) 445-. 



, relations. Schlomilch, O. Grunert 

 Arch. 9 (1847) 333-. 



Fractional coefficients. Barsotti, G. Lucca 

 At. Ac. 12 (1843) 411-. 



Game of draughts, problem. Lamarle, E. 

 [1852] Brux. Ac. Sc. Mm. 27 (1853) 

 47 pp. 



Gordian knot (bar and rings), theory. 

 Dassen, C. C. Arg. S. Ci. A. 44 (1897) 

 337-. 



jumping frog, arrangement of counters 



on board. Berg, F. J. van den. N. Arch. 



Wisk. 12 (1886) 38-; Fschr. Mth. (1885) 



121. 

 loto. Du Hays, . Liouv. J. Mth. 7 



(1842) 192-. 



played with 15 pieces on square board of 16 

 holes. Bellavitis, G. Yen. I. At. 6 (1880) 

 901-. 



of solitaire. Reiss, M. Crelle J. 54 (1857) 

 344-. 



. Hermary, . As. Fr. C. B. (1879) 



284-. 

 , as problem of analysis and situation. 



Suremain-de-Missery, A. Dijon Ac. Mm. 



(1841-42) 58-. 

 Grouping in games. Andre, D. Par. S. Phlm. 



Bll. 1 (1899) 139- ; 2 (1900) 45-, 77-. 



of instruments for simultaneous telegraphy. 

 Zetzsche, E. J. Tel. 15 (1891) 201-, 229-, 

 255-. 



problems, analytical treatment. Hoyer, P. 

 Mth. A. 50 (1898) 499-. 



Homogeneous products of n things of r dimen- 

 sions, proof. Walton, W. [1869] QJ. Mth. 

 10 (1870) 219-. 



Hyper-magic arithmetical spaces. Laisant, 

 C. A. Par. S. Mth. Bll. 22 (1894) 28-. 



squares, general limitations affecting. 

 Roberts, S. [1892] L. Mth. S. P. 24 (1893) 

 37-. 



La tour d'Hanoi (problem in permutations). 

 Allardice, R. E., & Eraser, A. Y. Edinb. 

 Mth. S. P. 2 (1884) 50-. 



Latin squares. Cayley, A. Mess. Mth. 19 

 (1890) 135-. 



, Euler's. Maillet, E. As. Fr. C. B. 



(1894) (Pt. 2) 244-. 



Magic cubes in n dimensions, way of represent- 

 ing in plane. Schlegel, . Par. S. Mth. 

 Bll. 20 (1892) 97-. 



cyclovolute. Nulty, E. [1834-44] Am. Ph. 

 S. T. 5 (1837) 205- ; 10 (1853) 17-. 



parallelepipeds. Harmuth, T. [1881] Arch. 

 Mth. Ps. 67 (1882) 238-. 



rectangles with odd numbers of sides. 

 Harmuth, T. Arch. Mth. Ps. 66 (1881) 

 413-. 



Magic squares. 



Moon, R. Camb. Mth. J. 4 (1845) 209-. 

 Clausen, T. Grunert Arch. 21 (1853) 97-. 

 Gyory, S. (xn) Mag. Ak. Ets. (1856) 77-. 

 Thompson, W. H. QJ. Mth. 10 (1870) 186-. 

 Drach, S. M. Mess. Mth. 2 (1873) 169-, 187. 

 Cayley, A. Mess. Mth. 6 (1877) 168. 

 Frisby, E. Wash. Ph. S. Bll. 3 (1880) 143-. 

 Marchand, D. Les Mondes 2 (1882) 106-, 



247-. 

 Rocquigny, F. [G.] de. Les Mondes 2 (1882) 



163. 



84 



