Outer product of vectors of permutations
outer.RdThe outer product of two vectors of permutations is the pairwise product of each element of the first with each element of the second.
Details
It works in much the same way as base::outer(). The third
argument, FUN, as in outer(X,Y,FUN="*") is regular
group-theoretic multiplication but can be replaced with + if you
are sure that the cycles of X and Y are distinct, see the
examples. Each element of the returned matrix is a one-element list.
The print method may have room for improvement.
Examples
(M <- outer(rperm(),rperm()))
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] permutation,7 permutation,7 permutation,7 permutation,7 permutation,7
#> [2,] permutation,7 permutation,7 permutation,7 permutation,7 permutation,7
#> [3,] permutation,7 permutation,7 permutation,7 permutation,7 permutation,7
#> [4,] permutation,7 permutation,7 permutation,7 permutation,7 permutation,7
#> [5,] permutation,7 permutation,7 permutation,7 permutation,7 permutation,7
#> [6,] permutation,7 permutation,7 permutation,7 permutation,7 permutation,7
#> [7,] permutation,7 permutation,7 permutation,7 permutation,7 permutation,7
#> [8,] permutation,7 permutation,7 permutation,7 permutation,7 permutation,7
#> [9,] permutation,7 permutation,7 permutation,7 permutation,7 permutation,7
#> [10,] permutation,7 permutation,7 permutation,7 permutation,7 permutation,7
#> [,6] [,7] [,8] [,9] [,10]
#> [1,] permutation,7 permutation,7 permutation,7 permutation,7 permutation,7
#> [2,] permutation,7 permutation,7 permutation,7 permutation,7 permutation,7
#> [3,] permutation,7 permutation,7 permutation,7 permutation,7 permutation,7
#> [4,] permutation,7 permutation,7 permutation,7 permutation,7 permutation,7
#> [5,] permutation,7 permutation,7 permutation,7 permutation,7 permutation,7
#> [6,] permutation,7 permutation,7 permutation,7 permutation,7 permutation,7
#> [7,] permutation,7 permutation,7 permutation,7 permutation,7 permutation,7
#> [8,] permutation,7 permutation,7 permutation,7 permutation,7 permutation,7
#> [9,] permutation,7 permutation,7 permutation,7 permutation,7 permutation,7
#> [10,] permutation,7 permutation,7 permutation,7 permutation,7 permutation,7
outer(cyc_len(4) + 0:3, cyc_len(4) + 100:101,"+") # OK because the cycles are distinct
#> [,1] [,2]
#> [1,] 1, 2, 3, 4, 101, 102, 103, 104 1, 2, 3, 4, 102, 103, 104, 105
#> [2,] 2, 3, 4, 5, 101, 102, 103, 104 2, 3, 4, 5, 102, 103, 104, 105
#> [3,] 3, 4, 5, 6, 101, 102, 103, 104 3, 4, 5, 6, 102, 103, 104, 105
#> [4,] 4, 5, 6, 7, 101, 102, 103, 104 4, 5, 6, 7, 102, 103, 104, 105
do.call("c",M) # c(M) gives a list and unlist(a) gives a numeric vector
#> [1] (1367) (15)(27)(36) (1352)(467) (134)(67) (26)(345)
#> [6] (1524736) (162453) (1357462) (176243) (1546327)
#> [11] (142)(3675) (136427) (146725) (14532)(67) (154326)
#> [16] (1365)(47) (16)(354) (146)(257) (176)(35) (13)(275)(46)
#> [21] (15)(2476) (47)(56) (1543)(26) (15)(246)(37) (164)(237)
#> [26] (2754) (1364)(27) (152643) (1273645) (34)(576)
#> [31] (253)(467) (1327546) (24)(67) (25367) (14365)
#> [36] (132647) (1265)(34) (24)(576) (1726534) (1356)(274)
#> [41] (13267) (15)(2763) (1356742) (134)(267) (345)
#> [46] (156)(2473) (12453) (135742) (17243) (15427)(36)
#> [51] (12)(34)(57) (17)(26)(34) (125)(37) (12)(457) (152476)
#> [56] (1723465) (1476)(235) (1256)(37) (16)(23574) (1753)(26)
#> [61] (26)(35) (13576) (27456) (26)(3475) (1725)(34)
#> [66] (13567)(24) (15)(2437) (2745) (124)(375) (136)(45)
#> [71] (12)(3465) (1346257) (12765) (12)(365)(47) (1752436)
#> [76] (1345)(267) (1437526) (1276) (1537426) (13)(256)
#> [81] (157)(2634) (1765)(234) (156372) (1574)(263) (2473)
#> [86] (1756)(34) (1473) (15372) (13)(457) (17)(2365)
#> [91] (15637)(24) (165)(2374) (15472)(36) (156324) (273)(46)
#> [96] (16)(3754) (173)(46) (1536472) (13)(456) (1652347)
#> [coerced from word form]