Affine Balanced Labellings - Revision history

Tedyun at 19:54, 4 February 2013

2013-02-04T19:54:05Z

2013-02-04T04:22:31Z

IDEAS

2013-01-29T02:43:46Z

IDEAS

2013-01-29T02:42:56Z

IDEAS

2013-01-24T16:56:47Z

2013-01-22T16:21:49Z

2013-01-21T21:08:21Z

IDEAS

2013-01-21T17:43:12Z

What are the restrictions?

2013-01-18T14:05:50Z

2013-01-18T02:14:22Z

@@ Line 11: / Line 11: @@
 # Only look at $3 \times 3$ sublattice.
 #* Among $2^9 = 512$ possible $3 \times 3$ patterns, 230 of them appears in permutations of size $\geq 6$. The actual number of patterns appearing in permutations of size 3, 4, 5, 6, 7, 8 is 6, 45, 143, 230, 230, 230.
-#* Conjecture: The number of $k\times k$ patterns in permutation diagrams of size $n \geq 2k$ is http://oeis.org/A048163. (verified: 2, 14, 230, 6902, 329462)
+#* Conjecture: The number of $k\times k$ patterns in permutation diagrams of size $n \geq 2k$ is http://oeis.org/A048163. (verified: 2, 14, 230, 6902, 329462) http://arxiv.org/pdf/1103.4884v1.pdf (Poly-Bernoulli numbers and lonesum matrices) http://www.sciencedirect.com/science/article/pii/S0012365X1200194X (Enumeration of (0,1)-matrices avoiding some 2×2 matrices)
 #* Conjecture: These numbers are also equal to the number of all $k\times k$ NW-patterns. (verified: 2, 14, 230, 6902, 329462, 22934774 are the number of NW patterns.)
 # Consider the matrix as an adjacency matrix of a graph, make a "diagram graph"

@@ Line 12: / Line 12: @@
 #* Among $2^9 = 512$ possible $3 \times 3$ patterns, 230 of them appears in permutations of size $\geq 6$. The actual number of patterns appearing in permutations of size 3, 4, 5, 6, 7, 8 is 6, 45, 143, 230, 230, 230.
 #* Conjecture: The number of $k\times k$ patterns in permutation diagrams of size $n \geq 2k$ is http://oeis.org/A048163. (verified: 2, 14, 230, 6902, 329462)
-#* Conjecture: These numbers are also equal to the number of all $k\times k$ NW-patterns. (verified: 2, 14, 230, 6902, 329462)
+#* Conjecture: These numbers are also equal to the number of all $k\times k$ NW-patterns. (verified: 2, 14, 230, 6902, 329462, 22934774 are the number of NW patterns.)
 # Consider the matrix as an adjacency matrix of a graph, make a "diagram graph"

@@ Line 12: / Line 12: @@
 #* Among $2^9 = 512$ possible $3 \times 3$ patterns, 230 of them appears in permutations of size $\geq 6$. The actual number of patterns appearing in permutations of size 3, 4, 5, 6, 7, 8 is 6, 45, 143, 230, 230, 230.
 #* Conjecture: The number of $k\times k$ patterns in permutation diagrams of size $n \geq 2k$ is http://oeis.org/A048163. (verified: 2, 14, 230, 6902, 329462)
-#* Conjecture: These numbers are also equal to the number of all $k\times k$ NW-pattern. (verified: 2, 14, 230, 6902, 329462)
+#* Conjecture: These numbers are also equal to the number of all $k\times k$ NW-patterns. (verified: 2, 14, 230, 6902, 329462)
 # Consider the matrix as an adjacency matrix of a graph, make a "diagram graph"

@@ Line 12: / Line 12: @@
 #* Among $2^9 = 512$ possible $3 \times 3$ patterns, 230 of them appears in permutations of size $\geq 6$. The actual number of patterns appearing in permutations of size 3, 4, 5, 6, 7, 8 is 6, 45, 143, 230, 230, 230.
 #* Conjecture: The number of $k\times k$ patterns in permutation diagrams of size $n \geq 2k$ is http://oeis.org/A048163. (verified: 2, 14, 230, 6902, 329462)
+#* Conjecture: These numbers are also equal to the number of all $k\times k$ NW-pattern. (verified: 2, 14, 230, 6902, 329462)
 # Consider the matrix as an adjacency matrix of a graph, make a "diagram graph"

@@ Line 12: / Line 12: @@
 #* Among $2^9 = 512$ possible $3 \times 3$ patterns, 230 of them appears in permutations of size $\geq 6$. The actual number of patterns appearing in permutations of size 3, 4, 5, 6, 7, 8 is 6, 45, 143, 230, 230, 230.
 #* Conjecture: The number of $k\times k$ patterns in permutation diagrams of size $n \geq 2k$ is http://oeis.org/A048163. (verified: 2, 14, 230, 6902, 329462)
 === What are the restrictions? ===

← Older revision		Revision as of 17:43, 21 January 2013
Line 27:		Line 27:
	677000 permutations examined. 267956 patterns so far.		677000 permutations examined. 267956 patterns so far.
	678000 permutations examined. 267956 patterns so far.		678000 permutations examined. 267956 patterns so far.
		+
		+
		+
		+	3150000 permutations examined. 329346 patterns so far.
		+	3155000 permutations examined. 329386 patterns so far.
		+	3160000 permutations examined. 329422 patterns so far.
		+	3165000 permutations examined. 329448 patterns so far.
		+	3170000 permutations examined. 329462 patterns so far.
		+	3175000 permutations examined. 329462 patterns so far.
		+	3180000 permutations examined. 329462 patterns so far.
		+	3185000 permutations examined. 329462 patterns so far.

← Older revision		Revision as of 14:05, 18 January 2013
Line 16:		Line 16:

	# NW condition		# NW condition
		+
		+
		+
		+	671000 permutations examined. 267910 patterns so far.
		+	672000 permutations examined. 267940 patterns so far.
		+	673000 permutations examined. 267955 patterns so far.
		+	674000 permutations examined. 267956 patterns so far.
		+	675000 permutations examined. 267956 patterns so far.
		+	676000 permutations examined. 267956 patterns so far.
		+	677000 permutations examined. 267956 patterns so far.
		+	678000 permutations examined. 267956 patterns so far.