diff --git a/Math/Sym.hs b/Math/Sym.hs
--- a/Math/Sym.hs
+++ b/Math/Sym.hs
@@ -20,6 +20,7 @@
     , toList          -- :: StPerm -> [Int]
     , fromList        -- :: [Int] -> StPerm
     , (/-/)           -- :: StPerm -> StPerm -> StPerm
+    , bijection       -- :: StPerm -> Int -> Int
     , unrankStPerm    -- :: Int -> Integer -> StPerm
     , sym             -- :: Int -> [StPerm]
 
@@ -50,6 +51,12 @@
     , ext             -- :: Perm a => Int -> a -> a
     , coshadow        -- :: (Ord a, Perm a) => a -> [a]
 
+    -- * Left-to-right maxima and similar functions
+    , lMaxima         -- :: Perm a => a -> Set
+    , lMinima         -- :: Perm a => a -> Set
+    , rMaxima         -- :: Perm a => a -> Set
+    , rMinima         -- :: Perm a => a -> Set
+
     -- * Simple permutations
     , simple          -- :: Perm a => a -> Bool
 
@@ -65,7 +72,7 @@
 import Data.List (sort, sortBy, group)
 import Data.Vector.Storable (Vector)
 import qualified Data.Vector.Storable as SV
-    ( Vector, toList, fromList, fromListN, empty, singleton
+    ( (!), Vector, toList, fromList, fromListN, empty, singleton
     , length, map, concat, splitAt
     )
 import qualified Math.Sym.Internal as I
@@ -124,6 +131,10 @@
       u' = SV.map ( + size v) $ toVector u
       v' = toVector v
 
+-- | The bijective function defined by a standard permutation.
+bijection :: StPerm -> Int -> Int
+bijection w = (SV.!) (toVector w)
+
 -- | @unrankStPerm n rank@ is the @rank@-th (Myrvold & Ruskey)
 -- permutation of @[0..n-1]@. E.g.,
 -- 
@@ -343,7 +354,8 @@
 shadow :: (Ord a, Perm a) => a -> [a]
 shadow w = map head . group $ sort [ del i w | i <- [0 .. size w - 1]]
 
--- | Insert a new largest element at the given position
+-- | Extend a permutation by inserting a new largest element at the
+-- given position
 ext :: Perm a => Int -> a -> a
 ext i = generalize' $ fromVector . ext0 . toVector
     where
@@ -356,6 +368,25 @@
 coshadow :: (Ord a, Perm a) => a -> [a]
 coshadow w = map head . group $ sort [ ext i w | i <- [0 .. size w]]
 
+
+-- Left-to-right maxima and similar functions
+-- ------------------------------------------
+
+-- | The set of indices of left-to-right maxima.
+lMaxima :: Perm a => a -> Set
+lMaxima = I.lMaxima . toVector . st
+
+-- | The set of indices of left-to-right minima.
+lMinima :: Perm a => a -> Set
+lMinima = I.lMaxima . I.complement . toVector . st
+
+-- | The set of indices of right-to-left maxima.
+rMaxima :: Perm a => a -> Set
+rMaxima = I.rMaxima . toVector . st
+
+-- | The set of indices of right-to-left minima.
+rMinima :: Perm a => a -> Set
+rMinima = I.rMaxima . 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
@@ -82,9 +82,9 @@
     , asc0    -- small ascents
     , des0    -- small descents
 
-    -- * List valued permutation statistics
-    , lminValues
-    , lminIndices
+    -- * Left-to-right maxima, etc
+    , lMaxima
+    , rMaxima
 
     -- * Sorting operators
     , stackSort
@@ -387,11 +387,11 @@
 last :: Perm0 -> Int
 last = SV.last
 
--- | The number of right-to-left minima.
+-- | The number of left-to-right minima.
 rmin :: Perm0 -> Int
 rmin = lmin . SV.reverse
 
--- | The number of right-to-left maxima.
+-- | The number of left-to-right maxima.
 rmax :: Perm0 -> Int
 rmax = lmax . SV.reverse
 
@@ -487,31 +487,30 @@
 des0 :: Perm0 -> Int
 des0 = stat c_des0
 
--- Vector valued permutation statistics
--- ----------------------------------
-
-foreign import ccall unsafe "stat.h lmin_values" c_lmin_values
-    :: Ptr CLong -> Ptr CLong -> CLong -> IO CLong
-
-foreign import ccall unsafe "stat.h lmin_indices" c_lmin_indices
-    :: Ptr CLong -> Ptr CLong -> CLong -> IO CLong
+-- Left-to-right maxima, etc
+-- -------------------------
 
-record :: (Ptr CLong -> Ptr CLong -> CLong -> IO CLong) -> Perm0 -> SV.Vector Int
-record f w = unsafePerformIO $ do
-               let n = SV.length w
-               v <- MV.unsafeNew n
-               SV.unsafeWith w $ \w_ptr ->
-                 MV.unsafeWith v $ \v_ptr -> do
-                   k <- f (castPtr v_ptr) (castPtr w_ptr) (fromIntegral n)
-                   SV.unsafeFreeze $ MV.unsafeSlice 0 (fromIntegral k) v
+-- | The list of indices of left-to-right maxima.
+lMaxima :: Perm0 -> SV.Vector Int
+lMaxima 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' = (SV.!) w (n-i)
+        if m' > m then do
+            MV.unsafeWrite v j (n-i)
+            (+1) `liftM` iter v (i-1) (j+1) m'
+          else
+            iter v (i-1) j m
 
--- | The list of values of left-to-right minima
-lminValues :: Perm0 -> SV.Vector Int
-lminValues = record c_lmin_values
+rMaxima :: Perm0 -> SV.Vector Int
+rMaxima w = SV.reverse . SV.map (\x -> SV.length w - x - 1) . lMaxima $ reverse w
 
--- | The list of indices of left-to-right minima
-lminIndices :: Perm0 -> SV.Vector Int
-lminIndices = record c_lmin_indices
 
 -- Sorting operators
 -- -----------------
diff --git a/Math/Sym/Stat.hs b/Math/Sym/Stat.hs
--- a/Math/Sym/Stat.hs
+++ b/Math/Sym/Stat.hs
@@ -46,8 +46,6 @@
     , dim         -- dimension
     , asc0        -- small ascents
     , des0        -- small descents
-    , lminValues
-    , lminIndices
     ) where
 
 import Prelude hiding (head, last)
@@ -57,9 +55,7 @@
     ( 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
-    , lminValues, lminIndices
     )
-import qualified Data.Vector.Storable as SV (toList)
 
 generalize :: Perm a => (Perm0 -> b) -> a -> b
 generalize f = f . toVector . st
@@ -185,11 +181,3 @@
 -- index @i@ such that @w[i] == w[i+1] + 1@.
 des0 :: Perm a => a -> Int
 des0 = generalize I.des0
-
--- | The list of values of left-to-right minima
-lminValues :: Perm a => a -> [Int]
-lminValues = generalize (SV.toList . I.lminValues)
-
--- | The list of indices of left-to-right minima
-lminIndices :: Perm a => a -> [Int]
-lminIndices = generalize (SV.toList . I.lminIndices)
diff --git a/cbits/stat.c b/cbits/stat.c
--- a/cbits/stat.c
+++ b/cbits/stat.c
@@ -320,38 +320,3 @@
 	}
 	return acc;
 }
-
-
-/* The array of left-to-right minima */
-long
-lmin_values(long *v, const long *w, long len)
-{
-	long m = *w + 1;
-	long acc = 0;
-
-	for (; len > 0; len--, w++) {
-		if (*w < m) {
-			m = *w;
-			acc++;
-			*(v++) = m;
-		}
-	}
-	return acc;
-}
-
-/* The array of indices of left-to-right minima */
-long
-lmin_indices(long *v, const long *w, long len)
-{
-	long i, m = *w + 1;
-	long acc = 0;
-
-	for (i = 0; i < len; i++, w++) {
-		if (*w < m) {
-			m = *w;
-			acc++;
-			*(v++) = i;
-		}
-	}
-	return acc;
-}
diff --git a/include/stat.h b/include/stat.h
--- a/include/stat.h
+++ b/include/stat.h
@@ -19,6 +19,3 @@
 long dim  (const long *, long); /* dimension */
 long asc0 (const long *, long); /* small ascents */
 long des0 (const long *, long); /* small descents */
-
-long lmin_values  (long *, const long *, long); /* values of left-to-right minima */
-long lmin_indices (long *, const long *, long); /* indices of left-to-right minima */
diff --git a/sym.cabal b/sym.cabal
--- a/sym.cabal
+++ b/sym.cabal
@@ -1,5 +1,5 @@
 Name:                sym
-Version:             0.3
+Version:             0.4
 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
@@ -168,6 +168,36 @@
 
 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
+          recordIndices w = [ head $ elemIndices x w | x <- g w ]
+
+prop_lMaxima = prop_record Sym.lMaxima lMaxima
+
+prop_lMinima = prop_record Sym.lMinima lMinima
+
+prop_rMaxima = prop_record Sym.rMaxima rMaxima
+
+prop_rMinima = prop_record Sym.rMinima rMinima
+
+prop_lMaxima_card =
+    forAll perm $ \w -> S.lmax w == SV.length (Sym.lMaxima w)
+
+prop_lMinima_card =
+    forAll perm $ \w -> S.lmin w == SV.length (Sym.lMinima w)
+
+prop_rMaxima_card =
+    forAll perm $ \w -> S.rmax w == SV.length (Sym.rMaxima w)
+
+prop_rMinima_card =
+    forAll perm $ \w -> S.rmin w == SV.length (Sym.rMinima w)
+
 segments :: [a] -> [[a]]
 segments [] = [[]]
 segments (x:xs) = segments xs ++ map (x:) (inits xs)
@@ -326,6 +356,14 @@
     , ("shadow",                         check prop_shadow)
     , ("coshadow",                       check prop_coshadow)
     , ("simple",                         check prop_simple)
+    , ("lMaxima",                        check prop_lMaxima)
+    , ("lMinima",                        check prop_lMinima)
+    , ("rMaxima",                        check prop_rMaxima)
+    , ("rMinima",                        check prop_rMinima)
+    , ("lMaxima/card",                   check prop_lMaxima_card)
+    , ("lMinima/card",                   check prop_lMinima_card)
+    , ("rMaxima/card",                   check prop_rMaxima_card)
+    , ("rMinima/card",                   check prop_rMinima_card)
     , ("unrankPerm",                     check prop_unrankPerm)
     , ("stackSort",                      check prop_stackSort)
     , ("stackSort/231",                  check prop_stackSort_231)
@@ -535,15 +573,6 @@
 
 prop_inv_21 = forAll perm $ \w -> S.inv w == length (Sym.copiesOf (Sym.st "21") w)
 
-prop_lmin_values =
-    forAll perm $ \w -> lMinima (st w) == S.lminValues w
-prop_lmin_indices =
-    forAll perm $ \w -> [ head $ elemIndices x w | x <- lMinima w ] == S.lminIndices w
-prop_lmin_card =
-    forAll perm $ \w -> and [ S.lmin w == length (S.lminValues w)
-                            , S.lmin w == length (S.lminIndices w)
-                            ]
-
 testsStat =
     [ ("asc",          check prop_asc)
     , ("des",          check prop_des)
@@ -573,9 +602,6 @@
     , ("asc0",         check prop_asc0)
     , ("des0",         check prop_des0)
     , ("inv/21",       check prop_inv_21)
-    , ("lmin/values",  check prop_lmin_values)
-    , ("lmin/indices", check prop_lmin_indices)
-    , ("lmin/card",    check prop_lmin_card)
     ]
 
 ---------------------------------------------------------------------------------