### Langford's Problem Bibliography

This has not been updated for years! --jm

- Combinatorische Aufgabe, Steiner, J., J. reine angew. Math., 1853, v45, 181-2, (Gesammelte Werke II, Berlin, 1882, 437-438)
- On certain distributions of integers in pairs with given differences, Skolem, Th., Math. Scand., 1957, v5, 57-68.
- PROBLEM, Langford, C. Dudley, Math. Gaz., 1958, v42, 228, poses problem, asks for theoretical treatment.
- Some Remarks on the triple systems of Steiner, Skolem, Th., Math. Scand., 1958, v6, 273-280.
- On Langford's Problem. I., Priday, C. J., Math. Gaz., 1959, v43, 250-3, proves all either hooked or perfect.
- On Langford's problem. II., Davies, Roy O., Math. Gaz., 1959, v43, 253-5, (2,n), n ≡ 0,-1 (mod 4), states problem of finding a function.
- A generalized Langford Problem., Gillespie & Utz, Fibonacci Quart., 1966, v4, #__, 184-6, proves L(3,n)=0 for n=2,3,4,5,6.
- A variant of Langford's Problem, Nickerson, R.S., American Math. Monthly, 1967, 74, 591-5, k-1 spaces between the two k's.
- The existence of Perfect 3-sequences, Levine, Eugene, Fibonacci Quart., 1968, v6, #5, 108-112.
- On the Generalized Langford's problem ?, Levine, Eugene, Fibonacci Quart., 1968, v6, #2, 135-8, some non-existence proofs for 2 classes of s & n.
- (a paper in the proceedings for a colloqium) Balatonfured?, Baron, G, Combinatorial theory & its applications, I., 1969, pp. 81-92, any group of n distinct, 1² k ² [s(n-1)/(s-1)]
- On generalized Langford sequences., Roselle & Thomasson, J. Combinatorial Theory, 1971, Ser. A, v11, 196-9, for (3,n), n ≡ -1,0,1 (mod 9)
- CORRESPONDENCE, Lloyd, P.R., Math. Gaz., 1971, v55, page 73, The 26 solutions to n=7 are given!
- The generalized Langford sequence., Saito & Hayasaka, Res. Rep. Miyagi Tech. College, 1975, #12, 93-8, explicit machine computation & programs.
- The extension of the generalized Langford sequence., Saito & Hayasaka, Res. Rep. Miyagi Tech. College, 1976, #13, 133-5, "where the same sets of s elements are permitted to occur any number of times."
- A perfect (s,n)-sequence based on F(k,i)., Saito & Hayasaka, Res. Rep. Miyagi Tech. College, 1977, #14, 101-8.
- The Langford (4,n)-sequence: a trigonometric approach., Saito & Hayasaka, Discrete Math., 1979, v28, #1, 81-8, 14 properties of Langford sequences. [This paper lists bogus solutions for Quadruplets, for n=16, 18, 19, and 20. The solutions to not check out!]
- Langford sequences: a progress report., Saito & Hayasaka, Math. Gaz., 1979, v63, #426, 261-2. This paper gives three confirmed solutions for L(4,24).
- Harmonic analysis of the Langford sequence., Saito, Sadao, Res. Rep. Miyagi Tech. College, 1980, #16, 99-103, a shift function closely related to Langford sequences
- A method of constructing Skolem and Langford sequences., Lorimer, Peter, Southeast Asian Bull. Math., 1982, v6, #2, 115-9.
- Theory of the perfect (s,n)-sequence based on F(i,k)., Saito & Hayasaka, Res. Rep. Miyagi Tech. College, 1983, #19, 73-80.
- Ladder graphs., Anderson, Ian, Ars Combinatoria, 1983, 16, A, 27-32, can be used to obtain... solutions to LP
- Langford Sequences: perfect and hooked., Simpson, James E., Discrete Math, 1983, v44, #1, 97-104.
- Exponential lower bounds for the number of Skolem and extremal Langford sequences., Abrham, Jaromir, Ars Combinatoria, 1986, 22, 187-198.
- Element Neighbourhoods in twofold triple systems., Colburn & Rosa, Journal of Geometry, 1987, v30, #1, 36-41.

Created by: John Miller, john@timehaven•us

Modified: 15-Oct-1988