|
| |
|
|
A213059
|
|
Subsets of positive integers arranged in canonical order.
|
|
1
|
|
|
|
1, 12, 2, 123, 13, 23, 3, 1234, 124, 134, 234, 14, 24, 34, 4, 12345, 1235, 1245, 1345, 2345, 125, 135, 145, 235, 245, 345, 15, 25, 35, 45, 5, 123456, 12346, 12356, 12456, 13456, 23456, 1236, 1246, 1256, 1346, 1356, 1456, 2346, 2356, 2456, 3456, 126, 136, 146, 156, 236, 246, 256, 346, 356, 456, 16, 26, 36, 46, 56, 6
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,2
|
|
|
COMMENTS
|
The order is self-explanatory (or see the Kubo-Vakil paper).
Of course once we reach subsets containing 10 this way of representing subsets by concatenation is unsatisfactory. Still, the sequence serves as a pointer to the Kubo-Vakil paper.
Sort by largest element, then decreasing size, then lexicographically (see Kubo-Vakil paper). - Michael S. Branicky, Jan 12 2021
|
|
|
LINKS
|
|
|
|
PROG
|
(Python)
from itertools import chain, combinations as C
def powerset(s): # in decreasing size
return chain.from_iterable(C(s, r) for r in range(len(s), -1, -1))
def agen():
m = 1 # largest element
while True:
for p in powerset(range(1, m)): yield int("".join(map(str, p+(m, ))))
m += 1
def aupton(terms):
alst, g = [], agen()
while len(alst) < terms: alst += [next(g)]
return alst
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
|
|
|
EXTENSIONS
|
|
|
|
STATUS
|
approved
|
| |
|
|
