A aUATEE DIMENSIONS. 



29 



* = 4 les cas r = O, r = I. Car, comme en oy) les cas ,? = 3, r = 3 

 et s = 3, /• = 4 et les cas s = 4^, r = 2 et s = 4, r = 3 se ramènent 

 à des nombres (r/^jSc),o fi l'aide des relations 



5c, c^ = 3c\ 







5c,/ = 





Nous dressons donc, 



d( 



3S résultats 







4 •' 



a ce,. 



= 1, 





a'c Va 



-0, 



5c^c" = 3c\ 

 5c,è^= é\ 



à. l'aide des dix-huit formules de 5/3) et 



d^c^Cg = 3 

 a.c-c,, = 1 



d'c c,, — 3 , 



arc Ca 



de 4û5/,, les deux tableaux complétants suivants: 



(4220) e. 



= 1 



(2330) 6v = 



8 



1 (1331)6-, 



= 16 



(4211)6-,. 



= 1 



(232l)6v = 



10 



(1322)6-, 



= 13 



(4112)c,. 



= 1 



(2312) 6-,= 



7 



(0530)6-, 



= 10 



(3320) c-. 



= 3 



(2222) cv = 



10 



(0521)6-, 



= 5 



(3311) c,. 



= 3 



(1520)6',= 



5 



(0440) 6-, 



= 10 



(3221) e,. 



= 5 



(1511)6-,= 



5 



(0431)6-, 



= 14 



(3212) r. 



= 4 



(1430) c, = 



12 



(0422) c. 



= 7 



(2420) c,. 



= 5 



(1421)6-,= 



12 



(0332)6-, 



= 12 



(241 l)r-. 



= 5 



(1412)6-, = 



rr' 







(3220) c. 



= 1 



(2221)6-,,= 



3 



(1321)6, 



= 4 



(321 l)c. 



= 1 



(1420)6-,= 



2 



(0430) c, 



= 4 



(2320) 6',, 



= 2 



(1411)c„ = 



2 



(0421)6-,, 



= 2 



(2311) c. 



= 2 



(1330)6-,,= 



4 



(0331) c„ 



= 4 



A l'aide de (-es triivaux préparatoires nous trouvons eirliu le 

 tableau des 



Nombres 6/''^'''/3''v-'V/''' = (f $'i^./r*')- 



(43301): 

 (34301): 

 (25301): 



(24401): 



(16301): 

 (15401): 

 (00401): 

 (05501): 

 (43211): 

 (34211): 

 (33311): 



1 



3 



5 



9 



5 



15 



15 



25 



1 



3 



5 



(25211): 



(24311) 



(16211): 



(15311) 

 (14411) 

 (06311) 



(05411): 



(43121) 



(42221): 



(34121) 



(33221): 



;j 

 1 1 



5 

 15 

 21 

 10 

 25 



1 



2 



3 



7 



(25121) 

 (24221) 

 (23321) 

 (16121) 

 (15221) 

 (14321) 

 (06221) 

 (05321) 

 (04421) 

 (42131) 

 (33131) 



= 5 

 = 13 



= 17 

 = 5 

 = 1 5 

 = 25 

 = 5 

 = 20 

 = 29 

 = 2 

 = () 



(32231): 



(2413J): 



(23231): 



(15131): 

 (14231): 

 (13331): 



(05231): 

 (04331): 



(41141): 

 (32141): 

 (23141): 



9 



(22241 



) = 17 



10 



(14141 



)=12 



18 



(13241 



) = 22, 



10 



(04241 



)=12 



22 



(03341 



) = 20 



28 



(31151 



)= 5 



10 



(22151, 



)= 10 



24 



(13151; 



= 10 



2 



(12251: 



= 15 



7 



(03251; 



= 10 



12 



(21161; 



= 5 1 



