Neil J. Calkin's Publications

Papers

1. Neil J. Calkin, "On the Number of Sum-free Sets", Bulletin of the London Mathematical Society 22 (1990), 141-146.

2. Neil J. Calkin and A. M. Frieze, "Probabilistic Analysis of a Parallel Algorithm for Finding Maximal Independent Sets", Random Structures and Algorithms 1 (1990), 39-50.

3. Neil J. Calkin, A. M. Frieze and Ł. Kucera, "On the Expected Performance of a Parallel Algorithm for Finding Maximal Independent Sets", Random Structures and Algorithms 3 (1992), 215-222.

4. Neil J. Calkin, A. M. Frieze and B. D. McKay, "On Subgraph Sizes in Random Graphs", Combinatorics, Probability and Computing 1 (1992), 123-134.

5. Neil J. Calkin, "A Curious Binomial Identity", Discrete Mathematics 131 (1994), 335-337.

6. Neil J. Calkin and Paul Erdős, "On a Class of Aperiodic Sum-free Sets", Mathematical Proceedings of the Cambridge Philosophical Society 120 (1996), 1-5.

7. Neil J. Calkin and Angela Taylor, "Counting Sets of Integers, no k of Which Sum to Another", Journal of Number Theory 57 (1996), Number 2, 323-327.

8. Neil J. Calkin and Steven R. Finch, "Conditions On Periodicity for a Sum-free Set", Experimental Mathematics 5 (1996), Number 2, 131-137.

9. Neil J. Calkin, "Dependent Sets of Constant Weight Vectors Over a Finite Field", Random Structures and Algorithms 9 (1996), Numbers 1 and 2, 49-53.

10. Neil J. Calkin and A. J. Granville, "On the Number of Co-prime-free Sets", Number Theory (New York 1991-1995) 9-18, Springer, New York, 1996.

11. Neil J. Calkin, "Dependent Sets of Constant Weight Binary Vectors", Combinatorics, Probability and Computing, 6 (1997), Number 3, 263-271.

12. Neil J. Calkin, Paul Erdős and Craig A. Tovey "New Ramsey Bounds From Cyclic Graphs of Prime Order", SIAM Journal of Discrete Math 10 (1997), Number 3, 381-387.

13. Neil J. Calkin and P. J. Cameron, "Almost Odd Random Sum-free Sets", Combinatorics, Probability and Computing, 7 (1998), Number 1, 27-32.

14. Neil J. Calkin and Herbert S. Wilf, "The Number of Independent Sets in a Grid Graph", SIAM Journal of Discrete Math, 11 (1998), Number 1, 54-60.

15. Neil J. Calkin and Jan McDonald Thomson, "Counting Generalized Sum-free Sets", Journal of Number Theory, 68 (1998), no.2, 151-159.

16. Neil J. Calkin, " Factors of Sums of Powers of Binomial Coefficients", Acta Arithmetica, 86 (1998), Issue 1, 17-26.

17. Neil J. Calkin, "On the Structure of a Random Sum-free Set", Discrete Math 190 (1998), Number 1-3, 247-257.

18. Neil J. Calkin, J. D. Key and M. J. De Resmini, "Minimum Weight and Dimension Formulas for some Geometric Codes", Designs, Codes and Cryptography 17, (1999), 105-120.

19. Neil J. Calkin, "On the Structure of a Random Sum-free Set", Discrete Math, Editors Choice for 1998 (Republishing of [17])

20. Neil J. Calkin and Herbert S. Wilf, "Recounting the Rationals", Amer. Math. Monthly 107 (2000), no. 4, 360-363.

21. Neil J. Calkin, E. Rodney Canfield and Herbert S. Wilf, "Averaging sequences, deranged mappings, and a problem of Lampert and Slater", J. Combin. Theory Ser. A 91 (2000), no. 1-2, 171-190.

22. Neil J. Calkin, Jonathan D. Edds and Douglas R. Shier, "Cancellation in Cyclic Consecutive Systems", Probabilistic Methods in Combinatorics and Combinatorial Optimization, J. Comput. Appl. Math. 142 (2002), no. 1, 13-26.

23. Neil J. Calkin and Jeffrey Farr, "Slow Convergence of a Double Biased Sequence", Congressus Numerantium, 159 (2002), 159-165.

24. Neil J. Calkin, Criel Merino, Steven Noble and M. Noy, "Improved Bounds for the Number of Forests and Acyclic Orientations in the Square Lattice", Electronic Journal of Combinatorics, 10 (1) (2003), R4.

25 Neil J. Calkin and Peter Dankelmann, "The Domatic Number of Regular Graphs", Ars Combinatoria, 73 (2004), 247--255.

26 Neil J. Calkin and John G. Stevens and Diana M. Thomas, "A Characterization for the Length of Cycles of the n-number Ducci Game", Fibonacci Quarterly, 43 (2005) no. 1, 53-59.

27 Neil J. Calkin, Steven R. Finch and Timothy B. Flowers, "Difference Density and Aperiodic Sum-free Sets", Integers 5 (2005) no. 2, A3, 10 pp.

28 Kim Bowman, Neil J. Calkin, Zach Cochran, Timothy Flowers, Kevin James, and Shannon Purvis, "Linear independence in a random binary vector model", Congr. Numer. 172 (2005), 29-32.

29 Morgan V. Brown, Neil J. Calkin, Kevin James, Adam J. King, Shannon Lockard, Robert C. Rhoades, "Trivial Selmer groups and even partitions of a graph", Integers 6 (2006), A33, 17 pp. (electronic).

30 Neil J. Calkin, Kevin James, Shannon Purvis, Shaina Race, Keith Schneider and Matthew Yancey, "Counting kings: as easy as &lambda₁, &lambda₂, &lambda₃,...", Proceedings of the Thirty-Seventh Southeastern International Conference on Combinatorics, Graph Theory and Computing. Congr. Numer. 183 (2006), 83-95.

31 Neil J. Calkin, Kevin James, Shannon Purvis, Shaina Race, Keith Schneider and Matthew Yancey, "Counting kings: explicit formulas, recurrence relations, and generating functions! Oh my!" Proceedings of the Thirty-Seventh Southeastern International Conference on Combinatorics, Graph Theory and Computing. Congr. Numer. 182 (2006), 41-51.

32 Neil J. Calkin, Jimena Davis, Kevin James, Elizabeth Perez and Charles Swannack, "Computing the integer partition function", Math. Comp. 76 (2007), no. 259, 1619-1638 (electronic).

33 Brittany Brown, Neil J. Calkin, Timothy B. Flowers, Kevin James, Ethan Smith and Amy Stout, "Elliptic Curves, Modular Forms and Sums of Hurwitz Class Numbers", Journal of Number Theory, 128 no .6, (2008), 1847-1863.

To appear

34 Jonathan M. Borwein, Neil J. Calkin and Dante Manna, "Euler Boole Summation Revisited", Amer. Math. Monthly, to appear.

35 Neil J. Calkin and Janine E. Janoski, "Matrices of Row and Column Sum 2", Cong. Numer., to appear.