1620 Permutations, combinations, etc. Binomial coefficients 1620 



Inequalities, theorem. Glaisher, J. W. L. 

 Mess. Mth. 8 (1879) 140-. 



of Tschebyscheff's (Cebysev), proof. Markov, 

 A. A. (xn) Kharkov Mth. S. Com. (1883) 

 105- ; Fschr. Mth. (1885) 168, 171. 



{(n-l)Sa 2 >2Sa&}. Grunert, J. A. Grunert 

 Arch. 26 (1856) 105-. 



ma m ~ l >^ -j-->mb m - 1 , proof and applica- 

 tions. Fort, 0. Schlomilch Z. 7 (1862) 

 46-. 



Inequality concerning sums of products of 

 numbers. Schiappa Monteiro, A. [1900] 

 Lisb. J. Sc. Mth. 6 (1902) 12-. 



, conditions, calculus. Navier, C. L. M. H. 

 Par. S. Phlm. Bll. (1825) 66-, 81-. 



, of, Fourier. Cournot, A. A. (\i 

 Adds.) Fe"russac Bll. Sc. Mth. 6 (1826) 1-. 



_ a2nf2 " 1 > !Ltl . Walton, W. Mess. Mth. 

 a (a 2n - 1) n 

 8 (1879) 130-. 



^1^ lies between^ a^and?^. Walker, 

 3fl-yl q q y 



G. F. [1882] Mess. Mth. 12 (1883) 37-. 



mx m ~ l (x - 1) ^ x m - 1 > m (x - 1) . Chrystal, 

 G. Edinb. Mth. S. P. 6 (1888) 29-. 



, a m b" + b m c n + c m a n > a n b m + b n c m + c n a m . 



Segar, H. W. Mess. Mth. 22 (1893) 47-. 

 Mean value. Holder, O. GStt. Nr. (1889) 38-. 



1620 Permutations, combinations, 

 partitions, distributions. Bi- 

 nomial and multinomial co- 

 efficients. 



Algorithms of arithmetical functions. Cesaro, 



E. G. Mt. 23 (1885) 175-. 

 Arithmetical cube. Laisant, C. A. As. Fr. 



C. B. (1891) (Ft. 2) 8-. 



tetrahedron. Laisant, C. A. Par. S. Mth. 

 Bll. 19 (1891) 18-. 



triangle, history. Fontes, . As. Fr. C. B. 



(1893) (Ft. 2) 236-. 



, properties. Laisant, C. A. As. Fr. 

 C. E. (1891) (Ft. 2) 1-; (1893) (Ft. 2) 

 206-. 



Arrangement of (1) cards, (2) counters : two 

 problems. Crelle, A. L. Crelle J. 44 (1852) 



15 counters in order, generalisation. 

 Malmsten, C.^J. Goteb. Hndl. 17 (1882) 77-. 



game (Josephspiel). Curtze, M. Bb. Mth. 



(1894) 116 ; (1895) 34-. 



(Josephus's problem), generalisation. 

 Tait, P. G. [1898] Edinb. B. S. P. 22 

 (1900) 165-. 



and probabilities, question. Tait, P. G. 

 Edinb. B. S. P. 8 (1873) 37-. 



in rows. Brunei, G. Bordeaux S. Sc. PV. 

 (1894-95) 28-. 



Arrangements, compound, question in. 



Sylvester, J. J. B. S. P. 12 (1862-63) 



561-. 

 , generalisation of theorem of Cauchy. 



Sylvester, J. J. Ph. Mg. 22 (1861) 378-. 



Arrangements, problem. Bouniakmcsky, V. 



[1857] St Pet. Ac. Sc. Bll. 16 (1858) 



67-. 

 , . Cayley, A. [1877] Edinb. B. S. P. 



9 (1878) 338-. 

 , . Tait, P. G. Edinb. B. S. P. 10 



(1880) 400-. 

 , Tait's problem. Muir, T. [1877] Edinb. 



B. S. P. 9 (1878) 382-. 

 , . Cayley, A. [1877] Edinb. B. S. 



P. 9 (1878) 388-. 

 , . Muir, T. [1881] Edinb. B. S. P. 



11 (1882) 187-. 

 of m things of one sort and n things of 



another sort, under conditions of priority. 



Whitworth, W. A. [1878] Mess Mth. 8 



(1879) 105-. 

 Binomial' 'calculus." Walsh, J. TillochPh. 



Mg. 63 (1824) 443-. 



BINOMIAL COEFFICIENTS. 



Euler, L. [1778] St Pet. Ac. Sc. N. Acta 



15 (1806) 33-. 

 Stockier, F. de B. G. Lisb. Mm. Ac. Sc. 2 



(1799) 480-. 



Pessuti, G. Mod. S. It. Mm. 11 (1804) 446-. 

 Mazio, N. G. Arcad. 22 (1824) 27-. 

 Arndt, F. Grunert Arch. 3 (1843) 256-. 

 Horta, F. Lisb. A. 2 (1858) 98-. 

 Le Tauniac, A. N. A. Mth. 20 (1861) 147-. 

 Lucas, E. N. A. Mth. 9 (1870) 308-. 

 Schlegel, S. F. V. Z. Mth. Ps. 23 (1878) 263-. 

 analytic faculties. Trudi, N. [1873] Nap. 



Ac. At. 6 (1875) No. 3, 16 pp. 

 Euler's theorem. Wolfers, J. P. Arch. Mth. 



Ps. 45 (1866) 411-. 



formulae. Tardy, P. G. Mt. 3 (1865) 1-. 

 . Delannoy, H. As. Fr. C. B. (1890) 



(Ft. 2) 35-. 

 a function of, and a series. Siacci, F. G. 



Mt. 10 (1872) 349-. 

 and their interpolation. Euler, L. St Pet. 



Ac. Sc. Mm. 9 (1824) 57-. 

 note. Busche, E. [1899] Hamb. Mth. Gs. 



Mt. 3 (1900) 379-. 

 properties. Schlomilch, 0. Grunert Arch. 1 



(1841) 431- ; 2 (1842) 434-. 

 . Tirelli, F. G. Mt. 14 (1876) 318-. 

 , and application to combinations. Baur, 



C. W. Z. Mth. Ps. 32 (1887) 218-. 

 derived from complex numbers. Studnicka, 



F. J. Prag Sb. (1877) 92-. 

 property. Zdrahal, A. Casopis 11 (*1882) 



47-; Fschr. Mth. (*1882) 190. 

 . Ekama, H. N. Arch. Wisk. 19 (1892) 



105- ; Fschr. Mth. (1892) 156. 

 in relation to gamma function and figurate 



numbers. Matthiessen, . D. Nf. Tbl. 



(*1868) 128- . 

 sum of series involving. Bonolis, A. G. Mt. 



11 (1873) 233-. 



n (n-l)(n-2) , . ,, 

 1 - + V gg ~ etc> derlved from 



expansion for cos nix. Schlomilch, 0. 

 Grunert Arch. 7 (1846) 46-. 



80 



