Bibliography
This is really a rough draft of an incomplete bibliography on
polyominoes, but I thought you might be interested.
Topics
Puzzles P, PT
General G
Enumeration E
convex EC
parallelogram
stack
directed
Tiling T
3-d polys
Triangles
Hexagons
Solid Polyomino Sets
If you are interested in a source for wooden pentacube sets, called
quintillions
and super quintillions, you should contact
Kadon Enterprises
1227 Lorene DR suite 16
Pasadena, MD 21122
(301) 437-2163.
In addition to quintillions and super quints they have a selection
of interesting
puzzles.
Abbreviations
JRM = Journal of Recreational Mathematics
Puzzles - 2 Dimensional
- [P91-1] Martin, George E. Polyominoes: A Guide to Puzzles and
Problems in Tiling, The Mathematical Association of America, 1991.
ISBN 0-88385-501-1
- [P79-1] Judd, R.L. and Zosel, M.E. ÒPentomino Alphanumerics,Ó
JRM Vol. 11 No. 3 1978-1979. p. 182-185.
- [P73-1] Mayer, Jean. ÒA Pentomino Problem,Ó JRM Vol. 6 No. 2 1973.
p. 105-108. [10x10 staircase]
- [P72-1] Verbakel, J.M.M. ÒThe F-Pentacube Problem,Ó JRM Vol. 5
No. 1 1972. p. 20-21. solid [pentomino puzzles]
- [P66-1] Gardner, Martin. ÒPolyominoes and Fault-Free RectanglesÓ
in New Mathematical Diversions from Scientific American, Simon
and Schuster, New York 1966. 150-161.
- [P65-1] Fletcher, John G. ÒA Program to Solve the Pentomino Problem
by the Recursive Use of Macros,Ó Communications of the ACM Vol.
8 No. 10 1965. p. 621-623. [computer solution to puzzle solving]
- [P59-1] Gardner, Martin. ÒPolyominoesÓ in Scientific American
Book Of Mathematical Puzzles and Diversions, Simon and Schuster,
New York, 1959, p.124-140 [pentomino, hexomino puzzles]
Puzzles - 3 Dimensional
- [PT73-2] Wagner, N.R. ÒConstructions with Pentacubes-2,Ó JRM Vol.
6 No. 3 1973. p. 211-214. [pentacube puzzles]
- [PT73-1] Whinihan, Michael J. and Trigg, Charles W. ÒParity and
Centerness Applied to the SOMA Cube,Ó JRM Vol. 6 No. 1 1973. p.
61-66. [SOMA cube puzzles]
- [PT72-1] Wagner, N.R. ÒConstructions with Pentacubes,Ó JRM Vol.
5 No. 4 1972. p. 266-268. [pentacube puzzles]
- [PT67-1] Bouwkamp, C. J. ÒCatalogue of solutions of the rectangular
3x4x5 solid pentomino problem.Ó 1967 The Netherlands. Technische
Hogeschool Edinhoven, Department of Mathematics, Edinhoven.
General Interest
[G65-1] Golomb, Solomon W. Polyominoes, Charles Scribner's Sons,
New York, 1965.
Enumeration of Polyominoes
[E91-2] Delest, M. Enumeration of polyominoes using MACSYMA. Theoretical
Computer Science 79 (1991) 209-226.
[E91-1] M. Delest. Polyominoes and Animals - Some Recent Results.
Journal of
Mathematical Chemistry V8 N1-3:3-18. Oct. 1991.
[E87-1] M. Delest, Enumeration of parallelogram polyominoes with
given bond and site
perimeter, Graphs Combin. 3 (1987) 325-339.
[E84-1] Delest, Marie-Pierre and Viennot, Gerard, Algebraic Languages
and Polyominoes
Enumeration, Theoretical Computer Science 34 (1984) 169-206
[E81-1] Klarner, David A. ÒMy Life Among The PolyominoesÓ in The
Mathematical
Gardner, 243-262. Wadsworth International, Belmont, CA 1981.
[E74-1] Klarner, D.A. and Rivest, R. Asymptotic bounds for the
number of convex n-
ominoes. Discrete Mathematics 8 (1974) 31-40.
[E73-1] Klarner, D.A. and Rivest, R.L. ÒA procedure for improving
the upper bound for
the number of n-ominoes.Ó Canadian Journal of Mathematics 25 (3)
(1973) 585-
602
[E72-1] Lunnon, W.F. ÒSymmetry of Cubical And General PolyominoesÓ
in Graph Theory
And Computing, Academic Press, London, 1972, p. 101-108
[E72-2] Lunnon, W.F. ÒCounting Hexagonal And Triangular PolyominoesÓ
in Graph
Theory And Computing, Academic Press, London, 1972, p. 87-100
[E71-1] Lunnon, W.F. ÒCounting PolyominoesÓ in Computers in Number
Theory, 347-
372, Academic Press, London 1971
[E69-1] Madachy, Joseph, Pentominoes -- Some Solved And Unsolved
Problems. JRM
V2 #3, 1969.
[E67-2] Klarner, D.A. Cell growth problems. Canadian Journal of
Mathematics 19 (1967)
851-863.
[E67-1] Parkin, T.R. and others, ÒPolyomino Enumeration Results,Ó
SIAM Fall Meeting,
1967.
[E62-1] Read, R.C. Contributions to the Cell Growth Problem. Canadian
Journal of
Mathematics 14 (1962) 1-20.
M. Delest and J.M. Fedou, Exact formulas for fully compact animals,
Rapport Interne LaBRIE,
Bordeaux, no 89-06
10. CONFERENCE PAPER
Delest, M.P.; Fedou, J.M.
Counting polyominoes using attribute grammars.
IN: Attribute Grammars and their Applications. International Conference
WAGA Proceedings. (Attribute Grammars and their Applications.
International
Conference WAGA Proceedings, Paris, France, 19-21 Sept. 1990).
Edited by:
Deransart, P.; Jourdan, M. Berlin, Germany: Springer-Verlag, 1990.
p.
46-60.
Abstract available.
Pub type: Theoretical or Mathematical.
Enumeration of Convex Polyominoes
[ECxx-1] M. Delest and S. Dulucq, Enumeration of directed column-convex
animals with
given perimeter and area, Rapport LaBRI, Bordeaux, no.87-15
[EC88-1] M. Delest, Generating function for column-convex polyominoes,
J. Combin
Theory Ser. A 48 (1) (1988) 12-31.
2. BOUSOUETMELOU M; VIENNOT XG.
HEAPS OF SEGMENTS AND Q-ENUMERATION OF DIRECTED CONVEX POLYOMINOES.
JOURNAL OF COMBINATORIAL THEORY SERIES A, 1992 JUL, V60 N2:196-224.
4. BOUSQUETMELOU M.
CONVEX POLYOMINOES AND HEAPS OF SEGMENTS.
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1992 APR 7, V25
N7:1925-1934.
5. BOUSQUETMELOU M.
CONVEX POLYOMINOES AND ALGEBRAIC LANGUAGES.
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1992 APR 7, V25
N7:1935-1944.
1. BOUSQUETMELOU M.
[CODING OF CONVEX POLYOMINOES AND EQUATIONS FOR THEIR ENUMERATION
ACCORDING TO AREA].
DISCRETE APPLIED MATHEMATICS, 1994 JAN 4, V48 N1:21-43.
Language: French.
2. BOUSQUETMELOU M.
[Q-ENUMERATION OF CONVEX POLYOMINOES].
JOURNAL OF COMBINATORIAL THEORY SERIES A, 1993 NOV, V64 N2:265-288.
Language: French.
6. BOUSQUETMELOU M.
[BIJECTION BETWEEN DIRECTED CONVEX POLYOMINOES AND BILATERAL DYCK
WORDS].
RAIRO-INFORMATIQUE THEORIQUE ET APPLICATIONS-THEORETICAL INFORMATICS
AND
APPLICATIONS, 1992, V26 N3:205-219.
Language: French.
1. CONFERENCE PAPER
Barcucci, E.; Pinzani, R.; Sprugnoli, R.
Directed column-convex polyominoes by recurrence relations.
IN: TAPSOFT '93: Theory and Practice of Software Development.
4th
International Joint Conference CAAP/FASE Proceedings. (TAPSOFT
'93: Theory
3. CONFERENCE PAPER
Beauquier, D.; Latteux, M.; Slowinski, K.
A decidability result about convex polyominoes.
IN: LATIN '92. 1st Latin American Symposium on Theoretical Informatics
Proceedings. (LATIN '92. 1st Latin American Symposium on Theoretical
Informatics Proceedings, Sao Paulo, Brazil, 6-10 April 1992).
Edited by:
Simon, I. Berlin, Germany: Springer-Verlag, 1992. p. 32-45.
Abstract available.
Pub type: Theoretical or Mathematical.
2. Domocos, V.; Hristea, F.
A codification of column-convex polyominoes which generates a
regular
language.
Bulletin of the European Association for Theoretical Computer
Science, June
1993 (no.50):197-208.
Abstract available.
Pub type: Theoretical or Mathematical.
Tiling
[T90-1] CONWAY JH; LAGARIAS JC.
TILING WITH POLYOMINOES AND COMBINATORIAL GROUP THEORY.
JOURNAL OF COMBINATORIAL THEORY SERIES A, 1990 MAR, V53 N2:183-
208.
[T91-1] BEAUQUIER D; NIVAT M.
ON TRANSLATING ONE POLYOMINO TO TILE THE PLANE.
DISCRETE & COMPUTATIONAL GEOMETRY, 1991, V6 N6:575-592.
[T93-1] LAGARIAS JC; ROMANO DS.
A POLYOMINO TILING PROBLEM OF THURSTON AND ITS
CONFIGURATIONAL ENTROPY. JOURNAL OF COMBINATORIAL THEORY SERIES
A,
1993 JUL, V63 N2:338-358.
11. CONFERENCE PAPER
Girault- Beauquier, D.; Nivat, M.
Tiling the plane with one tile (polyominoes).
IN: Proceedings of the Sixth Annual Symposium on Computational
Geometry.
(Proceedings of the Sixth Annual Symposium on Computational Geometry,
Berkeley, CA, USA, 6-8 June 1990). New York, NY, USA: ACM, 1990.
p. 128-38.
Abstract available.
Pub type: Theoretical or Mathematical.
12. Golomb, S.W.
Polyominoes which tile rectangles.
Journal of Combinatorial Theory, Series A, May 1989, vol.51, (no.1):117-24.
Abstract available.
Pub type: Theoretical or Mathematical.
Bitner, James. "Tiling 5n x 12 Rectangles with Y-Pentominoes."
JRM 7(4) 1974.
276-282
Reingold, Yao, and Sands. "Tiling with Incomparable Rectangles."
JRM 8(2)
1975-75. 112-119
Kramer, Earl. "Tiling Rectangles with T and C Pentominoes." JRM
16(2) 1983-
84. 102-113
Kramer, Earl and Gobel, Frits. "Tiling Rectangles with Pairs of
Pentominoes."
JRM 16(3) 1983-84. 198-206
Music
Just for fun:
[M69-1] Bedford, David. Pentomino. [London] Universal Edition
[c1969].
[music score]
Journal of Recreational Mathematics
[] Judd, R.L. and Zosel, M.E. "Pentomino Alphanumerics," JRM ?(3)
1978-79.
182-185.
Mayer, Jean. "A Pentomino Problem." JRM 6(2) 1973. 105-108.
Torbijn, Ir P.J. "The Unknown World of Octiamonds." JRM 7 (1)
1974. 1-7
Haselgrove, Jenifer. "Packing a Square with Y-Pentominoes." JRM
7(3) 1974.
229
Dekkers, A.J. "On a Problem of Dudeney's (letter)." JRM 7(4) 1974.
306-307
Barwell, Brian. "Clever Construction." JRM 8(2) 1975-76. 130
Gobel, F. and Jagers, A.A. "Generalized Coverings with Polyominoes."
JRM 9(4)
1976-77. 252-257
Philpott, Wade. "The Double-Double Pentomino Problem (letter)."
JRM 14(1)
1981-82. 61
Rosenheck, Bernard. "N-Omino Packing (solution)." JRM 14(1) 1981-82.
69-70
Meeus, Jean. "Tesselation II (solution)." JRM 14(3) 1981-82. 224-225
Liu, Andy. "Pentomino Problems." JRM 15(1) 1982-83. 8-13
Ohno, Yoshio. "Pentomino Packing II (problem)." JRM 15(2) 1982-83.
143
Nelson, Harry. "Hexomino Packing (solution)." JRM 15(2) 1982-83.
145
Harary, Frank and Weisbach, Michael. "Polycube Achievement Games."
JRM
15(4) 1982-83. 241-246
Waitsman, Michael. "Contact: A Game for Polyoid Boards." JRM 15(4)
1982-83.
257-266
Ohno, Yoshio. "Pentomino Packing (solution)." JRM 16(1) 1983-84.
65
Ohno, Yoshio. "Pentomino Packing II (solution)." JRM 16(2) 1983-84.
149-150
Coll, Pablo. "Pentomino Problem II (problem)." JRM 16(3) 1983-84.
221
Signmaster, David. "Polyomino Problem (problem)." JRM 16(3) 1983-84.
224
LIST OF REFERENCES "Vestpocket Bibliographies." JRM 16(4) 1983-84.
273-
275
Coll, Pablo. "Pentomino Problem III (problem)." JRM 16(4) 1983-84.
302
Kierstead, F.H. and Campbell, T.M. "A Pentomino Problem (solution)."
JRM
17(1) 1984-85. 75-77
readers. "Pentomino Problem II (solution)." JRM 17(3) 1984-85.
220-225
readers. "Polyomino Problem (solution)." JRM 17(3) 1984-85. 235-237
readers. "Pentomino Problem III (solution)." JRm 17(4) 1984-85.
310-311
Other References of Interest
Gardner, Martin. ÒPolycubesÓ in Knotted Doughnuts and Other Mathematical
Entertainments, Freeman, New York 1986. 28-43.
(also, pentomino puzzles)
Bouwkamp, C. J. ÒPacking a rectangular box with the twelve solid
pentominoes.Ó
1969. Journal of Combinatorial Theory 7: 278-280.
[xxx] Philpott, Wade E. ÒDomino and Superdomino Recreations -
Part 4,Ó JRM Vol. 5
No. 2 1972. p. 102-122.
[xxx] Philpott, Wade E. ÒDomino and Superdomino Recreations -
Part 5,Ó JRM Vol. 5
No. 3 1972. p. 177-196.
Eden, M. A two-dimensional growth process. Proc. 4th Berkeley
Symp. on Mathematical
Statistics and Probability, IV (Univ. of California Press, Berkeley,
1961) 223-239
Harary, Frank, ÒGraphical Enumeration Problems,Ó in Graph Theory
and Theoretical Physics,
Academic Press, London, 1967, p. 1-41
[applications to physics]
Klarner, D.A. Some results concerning polyominoes. Fibonacci Quarterly
3 (1965) 9-20.
Discrete Math 36 (1981) 246-264.
Golomb, Rec. Math Mag. 4,5,6,8 (1962) ÒGeneral Theory of PolyominoesÓ
Journal of C, I, SS: vol. 1 1976, p.1-8.
Publ. Math. Inst. Hungarian Acad. Sci. 5 (1960) 63-95
1. STEWART IN; WORMSTEIN A.
POLYOMINOES OF ORDER-3 DO NOT EXIST.
Pub type: Note.
JOURNAL OF COMBINATORIAL THEORY SERIES A, 1992 SEP, V61 N1:130-136.
3. BOUSQUETMELOU M.
[BIJECTION BETWEEN DIRECTED CONVEX POLYOMINOES AND BILATERAL DYCK
WORDS].
Language: French.
RAIRO-INFORMATIQUE THEORIQUE ET APPLICATIONS-THEORETICAL INFORMATICS
AND
APPLICATIONS, 1992, V26 N3:205-219.
7. BEAUQUIER D.
AN UNDECIDABLE PROBLEM ABOUT RATIONAL SETS AND CONTOUR WORDS OF
POLYOMINOES.
INFORMATION PROCESSING LETTERS, 1991 MAR 14, V37 N5:257-263.
3. LALANNE JC.
[PARALLELOGRAM POLYOMINOES WITH BORDERS AND BESSEL FUNCTIONS].
DISCRETE MATHEMATICS, 1993 MAY 15, V115 N1-3:217-230.
Language: French.
10. BEAUQUIER D.
AN UNDECIDABLE PROBLEM ABOUT RATIONAL SETS AND CONTOUR WORDS OF
POLYOMINOES.
INFORMATION PROCESSING LETTERS, 1991 MAR 14, V37 N5:257-263.
7. Beauquier, D.
An undecidable problem about rational sets and contour words of
polyominoes.
Information Processing Letters, 14 March 1991, vol.37, (no.5):257-63.
Abstract available.
Pub type: Theoretical or Mathematical.
1. Hands on pentominoes. Pal Alto, CA : Creative Publications,
c1986.
UCSB Main Lib QA459 .H295 1986 Curriculum Lab
2. Picciotto, Henri.
Pentomino activities lessons and puzzles / Henri Picciotto. Sunnyvale,
Calif. : Creative Publications, c1984-1986.
UCSB Main Lib QA459 .P52 1984 Curriculum Lab
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