Keep or discard some cycles of a permutation
keepcyc.RdGiven a permutation and a function that returns a Boolean specifying whether a cycle is acceptable, return a permutation retaining only the acceptable cycles.
Examples
keepcyc(rgivenshape(10,2:8),function(x){length(x) == 2}) # retains just transpositions
#> [1] (7,18) (32,35) (9,29) (13,30) (8,19) (23,25) (1,24) (3,32) (21,24)
#> [10] (10,14)
keepcyc(megaminx,function(x){any(x == 100)}) # retains just cycles modifying facet #100
#> White Purple DarkYellow
#> () () ()
#> DarkBlue Red DarkGreen
#> () () ()
#> LightGreen Orange LightBlue
#> () () ()
#> LightYellow Pink Grey
#> (100,102,104,106,108) () (74,86,98,100,112)
keepcyc(rperm(100),function(x){max(x)-min(x) < 3}) # retains just cycles with range<3
#> [1] (45) () () () (123)
#> [6] () () () (123) ()
#> [11] () () () () ()
#> [16] () () () () (57)
#> [21] () () () () (57)
#> [26] () (46) () () (13)
#> [31] () () (56) () (35)
#> [36] (35) () () () ()
#> [41] (35) (34) (123)(46)(57) (67) ()
#> [46] () (46) () () (45)
#> [51] () () () () ()
#> [56] () () () (56) (12)(34)(567)
#> [61] () () () (24) ()
#> [66] () () (35) () (13)
#> [71] (57) (24)(57) (34) (24) (23)
#> [76] () () () () ()
#> [81] () () () () ()
#> [86] () () (456) () ()
#> [91] (56) () () () ()
#> [96] () () () () ()
f <- function(x, p){all(x < p) || all(x > p)} # keep only cycles with all entries either
keepcyc(rgivenshape(9,rep(2:3,9)), f, p=20) # all < 20 or all >20
#> [1] (3,15)(10,17,16)(22,33)(24,37,35)(31,34)(36,43)
#> [2] (7,17)(14,19)(21,22,26)(23,42)(24,37)(30,43)(31,41)
#> [3] (1,8)(2,10)(11,12)(13,16,14)(21,34,35)(24,26)(27,42)(28,45,31)
#> [4] (24,45)(27,34)
#> [5] (3,4)(7,18,16)(28,36,45)(29,31)(30,34)(32,38)
#> [6] (1,19,17)(4,9,8)(21,44)(22,25,37)(26,43,30)(28,29)(34,42)
#> [7] (1,13)(2,7)(21,37)(22,33)(23,36)(24,26,29)(25,41,35)
#> [8] (3,12)(7,15)(10,17,18)(21,40)(22,35)(31,41)
#> [9] (4,11)(9,12)(22,25)(23,28)(24,42)(33,39,38)(34,41)