## Involve: A Journal of Mathematics

• Involve
• Volume 10, Number 3 (2017), 505-521.

### Tiling annular regions with skew and T-tetrominoes

#### Abstract

In this paper, we study tilings of annular regions in the integer lattice by skew and T-tetrominoes. We demonstrate the tileability of most annular regions by the given tile set, enumerate the tilings of width-2 annuli, and determine the tile counting group associated to this tile set and the family of all width-2 annuli.

#### Article information

Source
Involve, Volume 10, Number 3 (2017), 505-521.

Dates
Received: 23 February 2016
Accepted: 31 May 2016
First available in Project Euclid: 12 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.involve/1513087852

Digital Object Identifier
doi:10.2140/involve.2017.10.505

Mathematical Reviews number (MathSciNet)
MR3583879

Zentralblatt MATH identifier
1357.52020

Subjects
Primary: 52C20: Tilings in $2$ dimensions [See also 05B45, 51M20]

#### Citation

Bright, Amanda; Clark, Gregory; Dunn, Charles; Evitts, Kyle; Hitchman, Michael; Keating, Brian; Whetter, Brian. Tiling annular regions with skew and T-tetrominoes. Involve 10 (2017), no. 3, 505--521. doi:10.2140/involve.2017.10.505. https://projecteuclid.org/euclid.involve/1513087852

#### References

• J. H. Conway and J. C. Lagarias, “Tiling with polyominoes and combinatorial group theory”, J. Combin. Theory Ser. A 53:2 (1990), 183–208.
• M. P. Hitchman, “The topology of tile invariants”, Rocky Mountain J. Math. 45:2 (2015), 539–563.
• M. R. Korn, Geometric and algebraic properties of polyomino tilings, Ph.D. thesis, MIT, 2004, http://hdl.handle.net/1721.1/16628.
• C. Lester, “Tiling with T and skew tetrominoes”, Querqus: Linfield Journal of Undergraduate Research 1:3 (2012).
• C. Moore and I. Pak, “Ribbon tile invariants from the signed area”, J. Combin. Theory Ser. A 98:1 (2002), 1–16.
• R. Muchnik and I. Pak, “On tilings by ribbon tetrominoes”, J. Combin. Theory Ser. A 88:1 (1999), 188–193.
• I. Pak, “Ribbon tile invariants”, Trans. Amer. Math. Soc. 352:12 (2000), 5525–5561.
• S. Sheffield, “Ribbon tilings and multidimensional height functions”, Trans. Amer. Math. Soc. 354:12 (2002), 4789–4813.
• W. P. Thurston, “Conway's tiling groups”, Amer. Math. Monthly 97:8 (1990), 757–773.