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] (8,28) (1,28) (17,30) (22,31) (14,15) (11,21) (7,28) (7,34) (11,18)
#> [10] (7,28)
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] (12) () () () ()
#> [6] () () () (243)(56) ()
#> [11] (23) () (45) () ()
#> [16] () () (46) () ()
#> [21] () () (567) () (123)
#> [26] () () () () ()
#> [31] () () () () ()
#> [36] (57) () () () ()
#> [41] (57) () (46) () ()
#> [46] (13) () () (56) ()
#> [51] (35) (35) () () ()
#> [56] () (35) (34) (123)(46)(57) (67)
#> [61] () () (46) () ()
#> [66] (45) () () () ()
#> [71] () () () () (56)
#> [76] (12)(34)(567) () () () (24)
#> [81] () () () (35) ()
#> [86] (13) (57) (24)(57) (34) (24)
#> [91] (23) () () () ()
#> [96] () () () () ()
f <- function(x,p){all(x<p) || all(x>p)}
keepcyc(rgivenshape(9,rep(2:3,9)),f,p=20) # only cycles with all entries either <20 or >20
#> [1] (1,7)(9,17)(22,34)(27,36)(33,38,44)(35,41)
#> [2] (6,10)(22,34,32)(28,31)(33,39)
#> [3] (7,17)(14,19)(21,22,26)(23,42)(24,37)(30,43)(31,41)
#> [4] (1,8)(2,10)(11,12)(13,16,14)(21,34,35)(24,26)(27,42)(28,45,31)
#> [5] (24,45)(27,34)
#> [6] (3,4)(7,18,16)(28,36,45)(29,31)(30,34)(32,38)
#> [7] (1,19,17)(4,9,8)(21,44)(22,25,37)(26,43,30)(28,29)(34,42)
#> [8] (1,13)(2,7)(21,37)(22,33)(23,36)(24,26,29)(25,41,35)
#> [9] (3,12)(7,15)(10,17,18)(21,40)(22,35)(31,41)