@article{Barabash&Fraenkel&Weiss:1992,
	key = "Barabash, Fraenkel, and Weiss 1992",
	author = "A. Barabash and A. S. Fraenkel and B. Weiss",
	title = "Iterated {Beatty} functions",
	journal = RCD,
	volume = 1,
	year = "1992--3",
	pages = "333-348"}

@article{Komatsu:1995b,
	key = "Komatsu 1995b",
	author = "T. Komatsu",
	title = "On the characteristic word of the inhomogeneous {Beatty} sequence",
	journal = BAUSMS,
	volume = 51,
	year = "{\noopsort{1995b}}1995",
	pages = "337-351"}

@article{Zeeman:1986,
	key = "Zeeman 1986",
	author = "E. C. Zeeman",
	title = "Gears from the {Greeks}",
	journal = "Proc. Royal Institution (Great Britain)",
	volume = 58,
	year = 1986,
	pages = "137-156"}

@article{Faucheux:1926,
	key = "Faucheux 1926",
	author = "Faucheux",
	title = "Sur une question concernant des suites de nombres incommensurables",
	journal = NAM,
	volume = 1,
	year = 1926,
	pages = "237-239"}

@article{Tamura:1996,
	key = "Tamura 1996",
	author = "J. Tamura",
	title = "Certain sequences making a partition of the set
of positive integers",
	journal = ACTAMH,
	volume = 70,
	year = 1996,
	pages = "207-215"}

@article{Fraenkel:1994,
	key = "Fraenkel 1994",
	author = "A. S. Fraenkel",
	title = "Iterated floor function, algebraic numbers,
discrete chaos, {Beatty} subsequences, semigroups",
	journal = TAMS,
	volume = 341,
	year = 1994,
	pages = "639-664",
	comment = "checked"}

@article{Stolarsky:1996,
	key = "Stolarsky 1996",
	author = "K. B. Stolarsky",
	title = "Positive factors of {Wythoff} matrices",
	journal = SF,
	volume = 53,
	year = 1996,
	pages = "271-277"}

@article{Borwein&Borwein:1993,
	key = "Borwein and Borwein 1993",
	author = "J. M. Borwein and P. B. Borwein",
	title = "On the generating function of the integer
part: $[n \alpha + \gamma]$",
	journal = JNT,
	volume = 43,
	year = 1993,
	pages = "293-318",
	comment = "checked"}

@article{Bowman:1995,
	key = "Bowman 1995",
	author = "D. Bowman",
	title = "Approximation of $\lfloor n \alpha + s \rfloor$ and
the zero of $\lbrace n \alpha + s \rbrace$",
	journal = JNT,
	year = 1995,
	volume = 50,
	pages = "128-144",
	comment = "checked"}

@article{Davison:1981,
	key = "Davison 1981",
	author = "J. L. Davison",
	title = "Some remarks on {Beatty}-type sequences",
	journal = CN,
	volume = 30,
	year = 1981,
	pages = "257-263"}

@article{Horadam:1978,
	key = "Horadam 1978",
	author = "A. F. Horadam",
	title = "Wythoff pairs",
	journal = FQ,
	volume = 16,
	year = 1978,
	pages = "147-151",
	comment = "checked"}

@article{Stolarsky:1994,
	key = "Stolarsky 1994",
	author = "K. B. Stolarsky",
	title = "Certain sequences of {Wythoffian} matrices, and
maximal geometric progressions therein",
	journal = JCTA,
	volume = 68,
	year = 1994,
	pages = "361-371",
	comment = "checked"}

@article{Rosenblatt:1978,
	key = "Rosenblatt 1978",
	author = "J. Rosenblatt",
	title = "The sequence of greatest integers of an
arithmetic progression",
	journal = JLMS,
	volume = 17,
	year = 1978,
	pages = "213-218"}

@article{Boshernitzan&Fraenkel:1981,
	key = "Boshernitzan and Fraenkel 1981",
	author = "M. Boshernitzan and A. S. Fraenkel",
	title = "Nonhomogeneous spectra of numbers",
	journal = DM,
	volume = 34,
	year = 1981,
	pages = "325-327",
	comment = "checked"}

@article{Graham&Lin&Lin:1978,
	key = "Graham, Lin, and Lin 1978",
	author = "R. L. Graham and S. Lin and C.-S. Lin",
	title = "Spectra of numbers",
	journal = MMAG,
	volume = 51,
	year = 1978,
	pages = "174-176"}

@article{Fraenkel:1977,
	key = "Fraenkel 1977",
	author = "A. S. Fraenkel",
	title = "Complementary systems of integers",
	journal = AMM,
	volume = 84,
	year = 1977,
	pages = "114-115",
	comment = "checked"}

@article{Connell:1959a,
	key = "Connell 1959a",
	author = "I. G. Connell",
	title = "A generalization of {Wythoff's} game",
	journal = CMB,
	volume = 2,
	year = "{\noopsort{1959a}}1959",
	pages = "181-190"}

@article{Connell:1959b,
	key = "Connell 1959b",
	author = "I. G. Connell",
	title = "Some properties of {Beatty} sequences {I}",
	journal = CMB,
	volume = 2,
	year = "{\noopsort{1959b}}1959",
	pages = "190-197"}

@article{Szusz:1985,
	key = "{Sz\"usz} 1985",
	author = "P. {Sz\"usz}",
	title = "On a theorem of {Fraenkel}, {Levitt}, and {Shimshoni}",
	journal = DM,
	volume = 56,
	year = 1985,
	pages = "75-77",
	comment = "checked"}

@article{Berger&Felzenbaum&Fraenkel:1986,
	key = "Berger, Felzenbaum, and Fraenkel 1986",
	author = "M. A. Berger and A. Felzenbaum and A. S. Fraenkel",
	title = "Disjoint covering systems of rational {Beatty} sequences",
	journal = JCTA,
	volume = 42,
	year = 1986,
	pages = "150-153",
	comment = "checked"}

@article{deBruijn:1989,
	key = "de Bruijn 1989",
	author = "Bruijn, N. G. de",
	title = "Updown generation of {Beatty} sequences",
	journal = IM, 
	volume = 92,
	year = 1989,
	pages = "385-407"}

@article{Hendel&Monteferrante:1994,
	key = "Hendel and Monteferrante 1994",
	author = "R. J. Hendel and S. A. Monteferrante",
	title = "Hofstadter's extraction conjecture",
	journal = FQ,
	volume = 32,
	year = 1994,
	pages = "98-107",
	comment = "checked"}

@article{Coxeter:1953,
	key = "Coxeter 1953",
	author = "H. S. M. Coxeter",
	title = "The golden section, phyllotaxis, and {Wythoff's} game",
	journal = SM,
	volume = 19,
	year = 1953,
	pages = "135-143"}

@article{Silber:1976,
	key = "Silber 1976",
	author = "R. Silber",
	title = "A {Fibonacci} property of {Wythoff} pairs",
	journal = FQ,
	volume = 14,
	year = 1976,
	pages = "380-384",
	comment = "checked"}

@article{Connell:1960,
	key = "Connell 1960",
	author = "I. G. Connell",
	title = "Some properties of {Beatty} sequences {II}",
	journal = CMB,
	volume = 3,
	year = 1960,
	pages = "17-22"}

@article{Eggleton&Fraenkel&Simpson:1993,
	key = "Eggleton, Fraenkel, and Simpson 1993",
	author = "R. B. Eggleton and A. S. Fraenkel and R. J. Simpson",
	title = "{Beatty} sequences and {Langford} sequences",
	journal = DM,
	volume = 111,
	year = 1993,
	pages = "165-178"}

@article{Stolarsky:1991,
	key = "Stolarsky 1991",
	author = "K. B. Stolarsky",
	title = "From {Wythoff's} {Nim} to {Chebyshev's} inequality",
	journal = AMM,
	volume = 98,
	year = 1991,
	pages = "889-900",
	comment = "checked"}

@article{Porta&Stolarsky:1991,
	key = "Porta and Stolarsky 1991",
	author = "H. A. Porta and K. B. Stolarsky",
	title = "Wythoff pairs as semigroup invariants",
	journal = ADVM,
	volume = 85,
	year = 1991,
	pages = "69-82"}

@article{Fraenkel&Borosh:1973,
	key = "Fraenkel and Borosh 1973",
	author = "A. S. Fraenkel and I. Borosh",
	title = "A generalization of {Wythoff's} game",
	journal = JCTA,
	volume = 15,
	year = 1973,
	pages = "175-191",
	comment = "checked"}

@article{Fraenkel:1969,
	key = "Fraenkel 1969",
	author = "A. S. Fraenkel",
	title = "The bracket function and complementary sets of integers",
	journal = CJM,
	volume = 21,
	year = 1969,
	pages = "6-27"}

@article{Fraenkel&Kimberling:1994,
	key = "Fraenkel and Kimberling 1994",
	author = "A. S. Fraenkel and C. Kimberling",
	title = "Generalized {Wythoff} arrays, shuffles and interspersions",
	journal = DM,
	volume = 126,
	year = 1994,
	pages = "137-149",
	comment = "checked"}

@article{Kimberling:1997,
	key = "Kimberling 1997",
	author = "C. Kimberling",
	title = "Fractal sequences and interspersions",
	journal = AC,
	volume = 45,
	year = 1997,
	pages = "157-168"}

@article{Komatsu:1999a,
	key = "Komatsu 1999a",
	author = "T. Komatsu",
	title = "Substitution invariant inhomogeneous {Beatty} sequences",
	journal = TJM,
	volume = 22,
	year = "{\noopsort{1999a}}1999",
	pages = "235-243"}

@article{Tijdeman:2000,
	key = "Tijdeman 2000",
	author = "R. Tijdeman",
	title = "Fraenkel's conjecture for six sequences",
	journal = DM,
	volume = 222,
	year = 2000,
	pages = "223-234"}

@earticle{Pitman:2001,
	key = "Pitman 2001",
	author = "J. Pitman",
	title = "Sumsets of finite {Beatty} sequences",
	journal = EJC,
	volume = 8,
	number = 2,
	year = 2001,
	papernum = "\#R15",
	url = "http://www.combinatorics.org/Volume_8/Abstracts/v8i2r15.html"}