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 &lambda_{1}, &lambda_{2}, &lambda_{3},...", 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.