OFFSET
1,2
COMMENTS
The hexagonal graph has vertices which are the centers of identical regular hexagons tiling the plane and the centers of adjacent hexagons are connected. Alternatively, we can use an isomorphic representation in which the vertices are the elements of Z^2 and (x,y) is connected to (x-1,y),(x+1,y),(x,y-1),(x,y+1),(x-1,y-1),(x+1,y+1). A cluster of size t is a set of t points such that each pair of points of the set is on a connected path contained entirely within the set. A burst pattern is a labeling of Z^2 with 0's and 1's. The term a(n) denotes the number of different (up to a translation) burst patterns whose 1's are covered by a cluster of size n.
LINKS
M. Blaum, J. Bruck, and A. Vardy, Interleaving schemes for multidimensional cluster errors, IEEE Trans. on Inform. Theory 44(2) (1998), 730-743.
Tuvi Etzion and Alexander Vardy, Two-dimensional interleaving schemes with repetitions: constructions and bounds, IEEE Trans. on Inform. Theory, 48(2) (2002), 428-457.
Moshe Schwartz and Tuvi Etzion, Two-dimensional burst-correcting codes, Proceedings, International Symposium on Information Theory, 2004.
EXAMPLE
a(2) = 4 because we have the following burst patterns (the *'s indicate the 1's):
1) *
2) **
3) *
...*
4) .*
...*
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Tuvi Etzion and Moshe Schwartz (etzion(AT)cs.technion.ac.il), May 11 2004
STATUS
approved