From 21b4068e2570497b168c6b1038bd499f45ce473e Mon Sep 17 00:00:00 2001
From: Jeshiba <baconp@gmail.com>
Date: Fri, 23 Jun 2017 12:31:56 -0400
Subject: added robinsonSchensted and conversion to row words.

---
 Math/Combinatorics/.YoungTableaux.hs.swp | Bin 0 -> 12288 bytes
 Math/Combinatorics/YoungTableaux.hs      |  82 +++++++++++++++++++++++++++++--
 Math/Combinatorics/test.hs               |   4 ++
 3 files changed, 83 insertions(+), 3 deletions(-)
 create mode 100644 Math/Combinatorics/.YoungTableaux.hs.swp
 create mode 100644 Math/Combinatorics/test.hs

diff --git a/Math/Combinatorics/.YoungTableaux.hs.swp b/Math/Combinatorics/.YoungTableaux.hs.swp
new file mode 100644
index 0000000..0e4e515
Binary files /dev/null and b/Math/Combinatorics/.YoungTableaux.hs.swp differ
diff --git a/Math/Combinatorics/YoungTableaux.hs b/Math/Combinatorics/YoungTableaux.hs
index e365ee7..8964469 100644
--- a/Math/Combinatorics/YoungTableaux.hs
+++ b/Math/Combinatorics/YoungTableaux.hs
@@ -1,3 +1,37 @@
+type Tableau a = [[a]]
+--data SSYT a = S [[a]]
+type SSYT a = [[a]]
+type GT a = [[a]]
+
+--instance Show a => Show (SSYT a)
+  --where show (S xs) = show $ fst $ break null xs
+
+rowInsert :: Ord a => SSYT a -> a -> SSYT a
+rowInsert t = truncInfList . rowInsert' (t ++ (repeat []))
+
+rowInsert' :: Ord a => SSYT a -> a -> SSYT a
+rowInsert' t x = 
+  case break (>x) (head t) of
+    (r, []) -> (r ++ [x]):(tail t)
+    (r1, r2) -> (r1 ++ x:(tail r2)):(rowInsert' (tail t) (head r2))
+
+robinsonSchensted :: Ord a => [a] -> SSYT a
+robinsonSchensted = truncInfList . foldl rowInsert' (repeat [])
+
+truncInfList :: [[a]] -> [[a]]
+truncInfList = fst . break null
+
+toRowWord :: Ord a => SSYT a -> [a]
+toRowWord = concat . reverse
+
+{--
+rowInsert :: Ord a => SSYT a -> a -> SSYT a
+rowInsert (S t) x = 
+  case break (>x) (head t) of
+    (r, []) -> S $ (r ++ [x]):(tail t)
+    (r1, r2) -> let S s = rowInsert (S (tail t)) (head r2) in S $ (r1 ++ x:(tail r2)):s
+    --}
+
 isRowWord' :: Ord a => [a] -> [a] -> [a] -> Bool
 isRowWord' _  ys [] = ys == []
 isRowWord' [] [] zs = isRowWord' [head zs] [] (tail zs)
@@ -13,7 +47,49 @@ isRowWord = isRowWord' [] []
 reduceWord :: Ord a => [a] -> [a]
 reduceWord xs
   | length xs <= 2 = xs
-  | otherwise      = reduceWord' (reduceWord (init xs)) (last xs)
+  | otherwise      = let ys = reduceWord $ init xs in reduceWord' (init $ init ys) (last $ init ys, last ys, last xs) []
+  {-- | otherwise      = let ys = reduceWord $ init xs in 
+                     let (zs, ws) = splitAt (length ys - 2) ys in
+                       reduceWord'' zs (ws ++ [last xs]) --}
+
+reduceWord' :: Ord a => [a] -> (a, a, a) -> [a] -> [a]
+reduceWord' [] (u, v, w) ys =
+  if isRowWord (u:v:w:ys)
+    then u:v:w:ys
+    else if w < v && u <= v
+      then if u > w then u:w:v:ys
+                    else v:u:w:ys
+      else u:v:w:ys
+reduceWord' xs (u, v, w) ys =
+  if isRowWord $ xs ++ (u:v:w:ys)
+    then xs ++ (u:v:w:ys)
+    else if w < v && u <= v 
+      then if u > w then reduceWord' (init xs) (last xs, u, w) (v:ys)
+                    else reduceWord' (init xs) (last xs, v, u) (w:ys)
+      else reduceWord' (init xs) (last xs, u, v) (w:ys)
+
+prop_ReduceWord :: [Int] -> Bool
+prop_ReduceWord = isRowWord . reduceWord
+
+prop_ReduceWord' :: [Int] -> Bool
+prop_ReduceWord' xs = (length xs) == (length $ reduceWord xs)
+
+prop_ReduceWord_RobinsonSchensted :: [Int] -> Bool
+prop_ReduceWord_RobinsonSchensted xs = (toRowWord $ robinsonSchensted xs) == (reduceWord xs)
 
-reduceWord' :: Ord a => [a] -> a -> [a]
-reduceWord' xs x = 
+reduceWord'' :: Ord a => [a] -> [a] -> [a]
+reduceWord'' [] (u:v:w:ys) =
+  if isRowWord (u:v:w:ys)
+    then u:v:w:ys
+    else if w < v && u <= v
+      then if u > w then u:w:v:ys
+                    else v:u:w:ys
+      else u:v:w:ys
+reduceWord'' xs (u:v:w:ys) =
+  if isRowWord $ xs ++ (u:v:w:ys)
+    then xs ++ (u:v:w:ys)
+    else if w < v && u <= v 
+      then if u > w then reduceWord'' (init xs) (last xs:u:w:v:ys)
+                    else reduceWord'' (init xs) (last xs:v:u:w:ys)
+      else reduceWord'' (init xs) (last xs:u:v:w:ys)
+reduceWord'' xs ys = xs ++ ys
diff --git a/Math/Combinatorics/test.hs b/Math/Combinatorics/test.hs
new file mode 100644
index 0000000..490594c
--- /dev/null
+++ b/Math/Combinatorics/test.hs
@@ -0,0 +1,4 @@
+data Matrix a = M [[a]]
+
+instance Show a => Show (Matrix a)
+  where show (M xs) = show $ break (==[]) xs
-- 
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