I take it an n-ocylinder is a row of Pascal's triangle, then?
PWrong wrote:And many other shapes look like Pascal's triangle with a different starting point.
def numsum(a):
r = 0
for c in a:
r += int(c)
return r
def elemult(s, p):
r = []
for item in s:
r.append(item*p)
return r
def pascal(n, r = None):
if (r == None): r = []
i = len(r)
end = r[i-1]
while (i < n):
j = i-1
while (j > 0):
r[j] += r[j-1]
j -= 1
r.append(end)
i += 1
return r
def mfhs(r):
t = ''
ones = 0
twos = 0
HSlen = numsum(r)-len(r)+1
for c in r:
if (c == '1'):
ones += 1
elif (c == '2'):
twos += 1
else:
t += c
if (t == ''):
r = [1]
elif (len(t) == 1):
r = [1] + [0]*(int(t)-2) + [1]
elif (len(t) == 2):
r = [1] + [0]*(numsum(t)-3) + [1]
r[int(t[1])-1] += 1
r[len(r)-int(t[1])] += 1
else:
return None
if (twos): r = pascal(HSlen, r)
return elemult(r, 1<<ones)
PWrong wrote:Klein bottles and projective plains are asymmetric, but the n-torus is [1,n,1], so that's a counterexample.
The symmetry might relate to the fundamental polygon somehow.
Maybe the connected sum of shapes with symmetric homology also has symmetric homology.
So maybe non-orientable surfaces are asymmetric, and orientable surfaces are symmetric?
Also, what are the hole-sequences for the Möbius strip, the Klein bottle and the real projective plane?
What's the connected sum? I imagine it's not the same as the wedge sum as that one definitely introduces asymmetry.
PWrong wrote:The Mobius strip can deform into a circle, so it's [Z,Z].
Take a disk out of each shape, and glue them together at the boundary.
Users browsing this forum: No registered users and 11 guests