gh-38857: various small details in combinat

    
some of them are made to please the type-checker `mypy`

### 📝 Checklist

- [x] The title is concise and informative.
- [x] The description explains in detail what this PR is about.
- [ ] I have linked a relevant issue or discussion.
- [ ] I have created tests covering the changes.
- [ ] I have updated the documentation and checked the documentation
preview.
    
URL: #38857
Reported by: Frédéric Chapoton
Reviewer(s): David Coudert, Frédéric Chapoton

src/sage/combinat/alternating_sign_matrix.py

@@ -262,13 +262,12 @@ def to_monotone_triangle(self):
             True
         """
         n = self._matrix.nrows()
-        triangle = [None] * n
-        prev = zero_vector(ZZ, n)
+        triangle = [0] * n
+        add_row = zero_vector(ZZ, n)
         for j, row in enumerate(self._matrix):
-            add_row = row + prev
+            add_row = row + add_row
             triangle[n - 1 - j] = [i + 1 for i in range(n - 1, -1, -1)
                                    if add_row[i] == 1]
-            prev = add_row
         return MonotoneTriangles(n)(triangle)
 
     @combinatorial_map(name='rotate counterclockwise')

src/sage/combinat/lr_tableau.py

@@ -28,7 +28,7 @@
 #                  http://www.gnu.org/licenses/
 #****************************************************************************
 
-from itertools import zip_longest
+from itertools import zip_longest, accumulate
 
 from sage.categories.finite_enumerated_sets import FiniteEnumeratedSets
 from sage.combinat.tableau import SemistandardTableau, SemistandardTableaux
@@ -277,14 +277,15 @@ def is_littlewood_richardson(t, heights):
         False
     """
     from sage.combinat.words.word import Word
-    partial = [sum(heights[i] for i in range(j)) for j in range(len(heights)+1)]
     try:
         w = t.to_word()
     except AttributeError:  # Not an instance of Tableau
         w = sum(reversed(t), [])
+
+    partial = list(accumulate(heights, initial=0))
     for i in range(len(heights)):
         subword = Word([j for j in w if partial[i]+1 <= j <= partial[i+1]],
-                       alphabet=list(range(partial[i]+1,partial[i+1]+1)))
+                       alphabet=list(range(partial[i]+1, partial[i+1]+1)))
         if not subword.is_yamanouchi():
             return False
     return True
@@ -305,5 +306,5 @@ def _tableau_join(t1, t2, shift=0):
         sage: _tableau_join([[1,2]],[[None,None,2],[3]],shift=5)
         [[1, 2, 7], [8]]
     """
-    return [list(row1) + [e2+shift for e2 in row2 if e2 is not None]
-            for (row1, row2) in zip_longest(t1, t2, fillvalue=[])]
+    return [list(row1) + [e2 + shift for e2 in row2 if e2 is not None]
+            for row1, row2 in zip_longest(t1, t2, fillvalue=[])]

src/sage/combinat/multiset_partition_into_sets_ordered.py

@@ -251,8 +251,8 @@ def _repr_normal(self):
             string_parts = (str(sorted(k)) for k in self)
         else:
             string_parts = (str(sorted(k, key=str)) for k in self)
-        string_parts = ", ".join(string_parts).replace("[","{").replace("]","}")
-        return "[" + string_parts + "]"
+        string = ", ".join(string_parts).replace("[", "{").replace("]", "}")
+        return "[" + string + "]"
 
     def _repr_tight(self):
         r"""
@@ -670,7 +670,7 @@ def split_blocks(self, k=2):
         if not self:
             return {tuple([self]*k): 1}
 
-        out = {}
+        out: dict[tuple, int] = {}
         for t in product(*[_split_block(block, k) for block in self]):
             tt = tuple([P([l for l in c if l]) for c in zip(*t)])
             out[tt] = out.get(tt, 0) + 1

src/sage/combinat/output.py

@@ -738,7 +738,7 @@ def get_len(e):
                         st += ' '
                     if E_box:
                         st_num = str_tab[k-j][j]
-                        ln_left = int((len(st_num) - (len(st_num) % 2))/2)
+                        ln_left = len(st_num) // 2
                         st += st_num.rjust(row_height - 1 - ln_left + len(st_num), ' ').ljust(diag_length, ' ')
                     else:
                         st += ' ' * diag_length
@@ -761,12 +761,12 @@ def get_len(e):
     import re
     mm = min(len(re.search('^ +', l)[0]) for l in str_list) - 1
     str_list = [l[mm:].rstrip() for l in str_list]
-    while str_list[-1] == '':
+    while not str_list[-1]:
         str_list.pop()
     return "\n".join(str_list)
 
 
-def box_exists(tab, i, j):
+def box_exists(tab, i, j) -> bool:
     r"""
     Return ``True`` if ``tab[i][j]`` exists and is not ``None``; in particular this
     allows for `tab[i][j]` to be ``''`` or ``0``.

src/sage/combinat/shard_order.py

@@ -88,7 +88,7 @@ def __init__(self, p):
             Digraph on 3 vertices
         """
         self.runs = p.decreasing_runs(as_tuple=True)
-        self.run_indices = [None] * (len(p) + 1)
+        self.run_indices = [0] * (len(p) + 1)
         for i, bloc in enumerate(self.runs):
             for j in bloc:
                 self.run_indices[j] = i