Abstract
This article introduces spotlight tiling, a type of covering which is similar to tiling. The distinguishing aspects of spotlight tiling are that the “tiles” have elastic size, and that the order of placement is significant. Spotlight tilings are decompositions, or coverings, and can be considered dynamic as compared to typical static tiling methods. A thorough examination of spotlight tilings of rectangles is presented, including the distribution of such tilings according to size, and how the directions of the spotlights themselves are distributed. The spotlight tilings of several other regions are studied, and suggest that further analysis of spotlight tilings will continue to yield elegant results and enumerations.
Similar content being viewed by others
References
Golomb S.W.: Tiling with sets of polyominoes. J. Combin. Theory 9, 60–71 (1970)
Kasteleyn P.W.: The statistics of dimers on a lattice: I. the number of dimer arrangements on a quadratic lattice. Physica 27(12), 1209–1225 (1961)
Kenyon, R.W., Propp, J.G.,Wilson, D.B.: Trees and matchings. Electron. J. Combin. 7(1), #R25 (2000)
Propp J.: Enumeration of Matchings: Problems and Progress. In: Billera, L., Björner, A., Greene, C., Simion, R., Stanley, R.P. (eds) New Perspectives in Geometric Combinatorics, MSRI Publications, Vol. 38, pp. 255–291. Cambridge University Press, Cambridge (1999)
Sloane, N.J.A.: The on-line encyclopedia of integer sequences. published electronically at: http://www.research.att.com/~njas/sequences/.