diff --git a/Math/Sym.hs b/Math/Sym.hs
--- a/Math/Sym.hs
+++ b/Math/Sym.hs
@@ -57,6 +57,10 @@
     , rMaxima         -- :: Perm a => a -> Set
     , rMinima         -- :: Perm a => a -> Set
 
+    -- * Components and skew components
+    , components
+    , skewComponents
+
     -- * Simple permutations
     , simple          -- :: Perm a => a -> Bool
 
@@ -387,6 +391,19 @@
 -- | The set of indices of right-to-left minima.
 rMinima :: Perm a => a -> Set
 rMinima = I.rMaxima . I.complement . toVector . st
+
+
+-- Components and skew components
+---------------------------------
+
+-- | The set of indices of components.
+components :: Perm a => a -> Set
+components = I.components . toVector . st
+
+-- | The set of indices of skew components.
+skewComponents :: Perm a => a -> Set
+skewComponents = I.components . I.complement . toVector . st
+
 
 -- Simple permutations
 -- -------------------
diff --git a/Math/Sym/Internal.hs b/Math/Sym/Internal.hs
--- a/Math/Sym/Internal.hs
+++ b/Math/Sym/Internal.hs
@@ -77,6 +77,7 @@
     , rir     -- right-most increasing run
     , rdr     -- right-most decreasing run
     , comp    -- components
+    , scomp   -- skew components
     , ep      -- rank a la Elizalde & Pak
     , dim     -- dimension
     , asc0    -- small ascents
@@ -86,6 +87,9 @@
     , lMaxima
     , rMaxima
 
+    -- * Components
+    , components
+
     -- * Sorting operators
     , stackSort
     , bubbleSort
@@ -471,6 +475,10 @@
 comp :: Perm0 -> Int
 comp = stat c_comp
 
+-- | The number of skew components. 
+scomp :: Perm0 -> Int
+scomp = comp . complement
+
 -- | Rank as defined by Elizalde & Pak.
 ep :: Perm0 -> Int
 ep = stat c_ep
@@ -487,10 +495,11 @@
 des0 :: Perm0 -> Int
 des0 = stat c_des0
 
+
 -- Left-to-right maxima, etc
 -- -------------------------
 
--- | The list of indices of left-to-right maxima.
+-- | The set of indices of left-to-right maxima.
 lMaxima :: Perm0 -> SV.Vector Int
 lMaxima w = runST $ do
   v <- MV.unsafeNew n
@@ -508,10 +517,32 @@
           else
             iter v (i-1) j m
 
+-- | The set of indices of right-to-left maxima.
 rMaxima :: Perm0 -> SV.Vector Int
 rMaxima w = SV.reverse . SV.map (\x -> SV.length w - x - 1) . lMaxima $ reverse w
 
 
+-- Components
+-- ----------
+
+-- | The set of indices of components.
+components :: Perm0 -> SV.Vector Int
+components w = runST $ do
+  v <- MV.unsafeNew n
+  k <- iter v n 0 (-1)
+  SV.unsafeFreeze $ MV.unsafeSlice 0 k v
+    where
+      n = size w
+      {-# INLINE iter #-}
+      iter _ 0 _ _ = return 0
+      iter v i j m = do
+        let m' = max m $ (SV.!) w (n-i)
+        if m' == n-i then do
+            MV.unsafeWrite v j (n-i)
+            (+1) `liftM` iter v (i-1) (j+1) m'
+          else
+            iter v (i-1) j m'
+
 -- Sorting operators
 -- -----------------
 
@@ -536,6 +567,7 @@
 -- | One pass of bubble-sort.
 bubbleSort :: Perm0 -> Perm0
 bubbleSort = sortop c_bubblesort
+
 
 -- Single point deletions
 -- ----------------------
diff --git a/Math/Sym/Stat.hs b/Math/Sym/Stat.hs
--- a/Math/Sym/Stat.hs
+++ b/Math/Sym/Stat.hs
@@ -42,19 +42,21 @@
     , rir         -- right-most increasing run
     , rdr         -- right-most decreasing run
     , comp        -- components
+    , scomp       -- skew components
     , ep          -- rank a la Elizalde & Pak
     , dim         -- dimension
     , asc0        -- small ascents
     , des0        -- small descents
+    , shad        -- shadow
     ) where
 
 import Prelude hiding (head, last)
-import Math.Sym (Perm, toVector, st)
+import Math.Sym (Perm, toVector, st, shadow)
 import Math.Sym.Internal (Perm0)
 import qualified Math.Sym.Internal as I 
     ( asc, des, exc, fp, cyc, inv, maj, comaj, peak, vall, dasc, ddes
     , lmin, lmax, rmin, rmax
-    , head, last, lir, ldr, rir, rdr, comp, ep, dim, asc0, des0
+    , head, last, lir, ldr, rir, rdr, comp, scomp, ep, dim, asc0, des0
     )
 
 generalize :: Perm a => (Perm0 -> b) -> a -> b
@@ -159,6 +161,11 @@
 comp :: Perm a => a -> Int
 comp = generalize I.comp
 
+-- | The number of skew components. E.g., @[5,7,4,6,3,1,0,2]@ has three
+-- skew components: @[5,7,4,6]@, @[3]@ and @[1,0,2]@.
+scomp :: Perm a => a -> Int
+scomp = generalize I.scomp
+
 -- | The rank as defined by Elizalde and Pak [Bijections for
 -- refined restricted permutations, /J. Comb. Theory, Ser. A/, 2004]:
 -- 
@@ -181,3 +188,8 @@
 -- index @i@ such that @w[i] == w[i+1] + 1@.
 des0 :: Perm a => a -> Int
 des0 = generalize I.des0
+
+-- | The size of the shadow of @w@. That is, the number of different
+-- one point deletions of @w@.
+shad :: Perm a => a -> Int
+shad = length . shadow . st
diff --git a/sym.cabal b/sym.cabal
--- a/sym.cabal
+++ b/sym.cabal
@@ -1,5 +1,5 @@
 Name:                sym
-Version:             0.4
+Version:             0.4.1
 Synopsis:            Permutations, patterns, and statistics
 Description:         
   Definitions for permutations with an emphasis on permutation
diff --git a/tests/Properties.hs b/tests/Properties.hs
--- a/tests/Properties.hs
+++ b/tests/Properties.hs
@@ -168,11 +168,6 @@
 
 prop_coshadow = forAll (resize 50 perm) $ \w -> Sym.coshadow w == coshadow w
 
--- prop_lMaxima =
---     forAll perm $ \w -> SV.fromList (rMaxIndices w) == Sym.lMaxima w
---         where
---           rMaxIndices w = [ head $ elemIndices x w | x <- lMaxima w ]
-
 prop_record f g =
     forAll perm $ \w -> SV.fromList (recordIndices w) == f w
         where
@@ -198,6 +193,18 @@
 prop_rMinima_card =
     forAll perm $ \w -> S.rmin w == SV.length (Sym.rMinima w)
 
+-- The list of indices of components in a permutation
+components w = lMaxima w `cap` rMinima (bubble w)
+
+-- The list of indices of skew components in a permutation
+skewComponents w = components $ map (\x -> length w - x - 1) w
+
+prop_components =
+    forAll perm $ \w -> components (st w) == SV.toList (Sym.components w)
+
+prop_skewComponents =
+    forAll perm $ \w -> skewComponents (st w) == SV.toList (Sym.skewComponents w)
+
 segments :: [a] -> [[a]]
 segments [] = [[]]
 segments (x:xs) = segments xs ++ map (x:) (inits xs)
@@ -364,6 +371,8 @@
     , ("lMinima/card",                   check prop_lMinima_card)
     , ("rMaxima/card",                   check prop_rMaxima_card)
     , ("rMinima/card",                   check prop_rMinima_card)
+    , ("components",                     check prop_components)
+    , ("skewComponents",                 check prop_skewComponents)
     , ("unrankPerm",                     check prop_unrankPerm)
     , ("stackSort",                      check prop_stackSort)
     , ("stackSort/231",                  check prop_stackSort_231)
@@ -517,8 +526,11 @@
                             GT -> cap xs yt
 
 -- The number of components in a permutation
-comp w = length $ lMaxima w `cap` rMinima (bubble w)
+comp = length . components
 
+-- The number of skew components in a permutation
+scomp = length . skewComponents
+
 -- rank a la Elizalde
 ep = fst . last . filter (\(k,ys) -> all (k<=) ys) . zip [0..] . inits . st
 
@@ -542,6 +554,7 @@
 vall = length . valleys
 dasc = length . doubleAscents
 ddes = length . doubleDescents
+shad = length . shadow
 
 prop_asc   = forAll perm $ \w -> asc   w == S.asc   w
 prop_des   = forAll perm $ \w -> des   w == S.des   w
@@ -567,9 +580,11 @@
 prop_rir   = forAll perm $ \w -> rir   w == S.rir   w
 prop_rdr   = forAll perm $ \w -> rdr   w == S.rdr   w
 prop_comp  = forAll perm $ \w -> comp  w == S.comp  w
+prop_scomp = forAll perm $ \w -> scomp w == S.scomp w
 prop_dim   = forAll perm $ \w -> dim   w == S.dim   w
 prop_asc0  = forAll perm $ \w -> asc0  w == S.asc0  w
 prop_des0  = forAll perm $ \w -> des0  w == S.des0  w
+prop_shad  = forAll perm $ \w -> shad  w == S.shad  w
 
 prop_inv_21 = forAll perm $ \w -> S.inv w == length (Sym.copiesOf (Sym.st "21") w)
 
@@ -598,9 +613,11 @@
     , ("rir",          check prop_rir)
     , ("rdr",          check prop_rdr)
     , ("comp",         check prop_comp)
+    , ("scomp",        check prop_scomp)
     , ("dim",          check prop_dim)
     , ("asc0",         check prop_asc0)
     , ("des0",         check prop_des0)
+    , ("shad",         check prop_shad)
     , ("inv/21",       check prop_inv_21)
     ]