Publications of Robert Gardner housed on the ETSU Server

This website is no longer updated (effective May 2024)! The papers listed here are housed on the ETSU server and are subject to deletion at some point in the future. See the Publications of Robert Gardner page for versions of the papers posted on Google Drive, which should be permanently available.

Discrete Mathematics
  1. R. Calahan and R. Gardner, 3-Transrotational Steiner Triple Systems, Congressus Numerantium, 81 (1991) 65-68 (MR#1152035).
  2. R. Gardner, Steiner Triple Systems with Near-Rotational Automorphisms, Journal of Combinatorial Theory - Series A, 61(2) (1992) 322-327 (MR#1185002).
  3. R. Gardner, Transrotational Directed Triple Systems, Congressus Numerantium, 90 (1992) 97-102 (MR#1208967).
  4. R. Calahan and R. Gardner, A Special Case of Bicyclic Steiner Triple Systems, Congressus Numerantium, 88 (1992) 77-80 (MR#1208920).
  5. R. Gardner, A Note on a Class of Steiner Triple Systems, Ars Combinatoria, 36 (1993) 157-160 (MR#1246908).
  6. R. Calahan and R. Gardner, Bicyclic Steiner Triple Systems, Discrete Mathematics, 128 (1994) 35-44 (MR#1271854).
  7. R. Gardner, Steiner Triple Systems with Transrotational Automorphisms, Discrete Mathematics, 131 (1994) 99-104 (MR#1287725).
  8. R. Gardner, Near-Rotational Directed Triple Systems, Ars Combinatoria, 38 (1994) 137-143 (MR#1310413).
  9. D. Bryant, S. El-Zanati, and R. Gardner, Decompositions of Km,n and Kn into Cubes, Australasian Journal of Combinatorics, 9 (1994) 285-290 (MR#1271208).
  10. G. Coker and R. Gardner, Some Rotational Automorphisms of Mendelsohn Triple and Quadruple Systems, Utilitas Mathematica, 47 (1995) 117-127 (MR#1330892).
  11. G. D. Coker, R. Gardner and R. Johnson, Decompositions of the Complete Digraph and the Complete Graph which admit certain Automorphisms, Congressus Numerantium, 108 (1995) 65-84 (MR#1369277).
  12. R. Gardner, P. Torbett and A. Weems, Decompositions of the Complete Digraph into each of the Orientations of a 4-Cycle which admit a Certain Automorphism, Congressus Numerantium, 120 (1996) 33-39 (MR#1431953).
  13. R. Gardner and R. Zijlstra, Reverse Directed Triple Systems, Journal of Combinatorial Mathematics and Combinatorial Computing, 21 (1996) 179-186 (MR#1395952).
  14. R. Calahan-Zijlstra, R. Gardner, B. Micale, and M. Pennisi, Cyclic and Rotational Hybrid Triple Systems, Discrete Mathematics, 171 (1997) 121-139 (MR#1454445) and Discrete Mathematics, 175 (1997) 143-161 (MR#1475844).
  15. R. Gardner, Optimal Packings and Coverings of the Complete Directed Graph with 3-Circuits and with Transitive Triples, Congressus Numerantium, 127 (1997) 161-170 (MR#1605003).
  16. R. Gardner, Bicyclic Directed Triple Systems, Ars Combinatoria, 49 (1998) 249-257 (MR#1633131).
  17. R. Gardner, Bicyclic Decompositions of Kv into copies of K3 È {e}, Utilitas Mathematica, 54 (1998) 51-57 (MR#1658161).
  18. R. Gardner, Triple Systems from Mixed Graphs, Bulletin of the Institute of Combinatorics and its Applications, 27 (1999) 95-100 (MR#1713567).
  19. R. Gardner, C. Huff, and J. Kennedy, Decompositions and Packings of Digraphs with Orientations of 4-Cycles, Ars Combinatoria, 54 (2000) 269-282 (MR#1742422).
  20. G. Coker, R. Gardner, P. Torbett and A. Weems, Bicyclic Decompositions of the Complete Digraph into Orientations of a 4-Cycle, Journal of Combinatorial Mathematics and Combinatorial Computing, 37 (2001) 43-52 (MR#1834430).
  21. R. Gardner, Cyclic and Rotational Decompositions of Kn into Stars, Ars Combinatoria, 61 (2001) 313-318 (MR#1863390).
  22. G. Chapman and R. Gardner, Decompositions of Uniform Complete Directed Multigraphs Into Each of the Orientations of a 4-Cycle, Journal of Combinatorial Mathematics and Combinatorial Computing, 39 (2001) 183-201 (MR#1865856).
  23. R. Gardner and K. Proffitt, Decomposing and Packing the Complete Graph with Osculating 4-Cycles, Congressus Numerantium, 153 (2001) 65-76 (MR#1887470).
  24. L. Brown, G. Coker, R. Gardner, and J. Kennedy, Packing the Complete Bipartite Graph with Hexagons, Congressus Numerantium, 174 (2005) 97-106 (MR#2193958).
  25. B. Bobga and R. Gardner, Bicyclic, Rotational, and Reverse Mixed Triple Systems, Bulletin of the Institute of Combinatorics and Its Applications, 48 (2006), 45-52 (MR#2259701).
  26. R. Gardner, C. Gwellem, and J. Lewenczuk, Maximal Cyclic 4-Cycle Packings and Minimal Cyclic 4-Cycle Coverings of the Complete Graph, Congressus Numerantium, 180 (2006), 193-199 (MR#2311260).
  27. R. Gardner and T. Holt, Decompositions of the Complete Symmetric Digraph into Orientations of the 4-Cycle with a Pendant Edge, Congressus Numerantium, 190 (2008), 173-182(MR#2489800) .
  28. R. Gardner, Q. Tran, and R. Zijlstra, Tricyclic Steiner Triple Systems, Graphs and Combinatorics, 26 (2010), 31-42 (MR#2606616).
  29. R. Gardner, S. Lavoie, C. Nguyen, 4-Cycle Coverings of the Complete Graph with a Hole, International Journal of Pure and Applied Mathematics, 64(2) (2010), 317-339 (MR#2757322).
  30. D. Cantrell, G. Coker, and R. Gardner, Cyclic, f-Cyclic, and Bicyclic Decompositions of the Complete Graph into the 4-Cycle with a Pendant Edge, Utilitas Mathematica, 87 (2012), 245-253 (MR#2920000).
  31. B. Coker, G.D. Coker, and R. Gardner, Decompositions of Various Complete Graphs into isomorphic Copies of the 4-Cycle with a Pendant Edge, International Journal of Pure and Applied Mathematics, 74(4) (2012) 485-492.
  32. R. Beeler, R. Gardner, C. Gwellem, and J. Lewenczuk, Decompositions, Packings, and Coverings of the Complete Digraph with Orientations of K3 ∪ {e}, Utilitas Mathematica, 100 (2016), 153-167 (MR#3526661)
  33. B. Coker, G. Coker, R. Gardner, and Y. Xia, Packings and Coverings of Various Complete Graphs with the 4-Cycle with a Pendant Edge, ISRN Combinatorics, Volume 2013 (2013), Article ID 236298, 8 pages.
  34. R. Gardner and W. Surber, Restricted and Unrestricted Hexagon Coverings of the Complete Bipartite Graph, Congressus Numerantium, 217 (2013), 107-128 (MR#3220298).
  35. C. Culver and R. Gardner, Decompositions of the Complete Mixed Graph into Mixed Stars, International Journal of Innovation in Science and Mathematics, 8(3) (2020), 110-114.
  36. R. Gardner and K. Kosebinu, Decompositions of the λ-Fold Complete Mixed Graph into Mixed 6-Stars, AppliedMath, 4(1), 211-224. Additional information is on the journal webpage.
  37. R. Gardner and S. Ignace, Mixed Hexagon Systems, Bulletin of the Institute of Combinatorics and Its Applications, to appear.
Complex Analysis
  1. R. Gardner and N. K. Govil, Inequalities Concerning the Lp Norm of a Polynomial and its Derivative, Journal of Mathematical Analysis and Applications, 179(1) (1993) 208-213 (MR#1244959).
  2. R. Gardner and N. K. Govil, On the Location of the Zeros of a Polynomial, Journal of Approximation Theory, 78 (1994) 286-292 (MR#1285264).
  3. R. Gardner and N. K. Govil, An Lp Inequality for a Polynomial and its Derivative, Journal of Mathematical Analysis and Applications, 193(2) (1995) 490-496 (MR#1338718), and 194(3) (1995) 720-726 (MR#1350192).
  4. R. Gardner and N. K. Govil, Some Inequalities for Entire Functions of Exponential Type, Proceedings of the American Mathematical Society, 123(9) (1995) 2757-2761 (MR#1257107).
  5. R. Gardner and N. K. Govil, Some Inequalities for Maximum Modulus of Polynomials, Journal of Orissa Mathematical Society, 12-15 (1993-96) 135-140.
  6. R. Gardner and N. K. Govil, Some Generalizations of the Eneström-Kakeya Theorem, Acta Mathematica Hungarica, 74(1-2) (1997) 125-134 (MR#1428052).
  7. R. Gardner and N. K. Govil, Functions of Exponential Type Not Vanishing in a Half-Plane, Analysis, 17 (1997) 395-402 (MR#1600342).
  8. R. Gardner and A. Weems, A Bernstein Type Lp Inequality for a Certain Class of Polynomials, Journal of Mathematical Analysis and its Applications, 219 (1998) 472-478 (MR#1606366).
  9. J. Cao and R. Gardner, Restrictions on the Zeros of a Polynomial as a Consequence of Conditions on the Coefficients of Even and Odd Powers of the Variable, Journal of Computational and Applied Mathematics, 155(1) (2003) 153-162 (MR#1992295).
  10. R. Gardner, N. K. Govil, and A. Weems, Growth of Polynomials not Vanishing Inside a Circle, International Journal of Pure and Applied Mathematics, 13(4) (2004), 491-498 (MR#2068722).
  11. R. Gardner, N. K. Govil, and A. Weems, Some Results Concerning Rate of Growth of Polynomials, East Journal of Approximations, 10(3) (2004), 301-312 (MR#2076890).
  12. A. Lin, B. Huang, J. Cao, R. Gardner, Some Results on the Location of Zeros of Analytic Functions, Chinese Journal of Engineering Mathematics, 21(5) (2004), 785-791 (MR#2107731).
  13. R. Gardner, N.K. Govil, and S. R. Musukula, Rate of Growth of Polynomials not Vanishing Inside a Circle, Journal of Inequalities in Pure and Applied Mathematics, 6(2) (2005), Article 53, 9 pp (electronic) (MR#2150907).
  14. Atif Abueida and R. Gardner, Some Generalizations of the Eneström-Kakeya Theorem, Theory of Polynomials and Applications, in Theory of Polynomials and Applications, Recent Advances, ed. K.K. Dewan, New Dehli: Deep & Deep Publications (2007), 1-10.
  15. R. Gardner and B. Shields, The Number of Zeros of a Polynomial in a Disk, Journal of Classical Analysis, 3(2) (2013), 167-176 (MR#3322267).
  16. R. Gardner and N. K. Govil, The Eneström-Kakeya Theorem and Some of Its Generalizations, in Current Topics in Pure and Computational Complex Analysis, ed. S. Joshi, M. Dorff, and I. Lahiri, New Delhi: Springer-Verlag (2014), 171-200 (MR#3329717).
  17. R. Gardner and B. Shields, The Number of Zeros of a Polynomial in a Disk as a Consequence of Restrictions on the Coefficients, Acta et Commentationes Universitatis Tartuensis de Mathematica 19(2) (2015), 109-120 (MR#3448640).
  18. D. Bryant and R. Gardner, Results on the Number of Zeros in a Disk for Three Types of Polynomials, Acta et Commentationes Universitatis Tartuensis de Mathematica 20(2) (2016), 135-149 (MR#3589215).
  19. W. "Ty" Frazier and R. Gardner, An Eneström-Kakeya Theorem for New Classes of Polynomials, Acta et Commentationes Universitatis Tartuensis de Mathematica, 23(1) (2019), 103-115 (MR#3998013).
  20. N. Carney, R. Gardner, R. Keaton, and A. Powers, The Eneström-Kakeya Theorem for Polynomials of a Quaternionic Variable, Journal of Approximation Theory, Volume 250 (February 2020) as Article 105325 (MR#4035962).
  21. G. M. Sofi, S. A. Ahanger, and R. Gardner, Some Classes of Polynomials Satisfying Sendov's Conjecture, Studia Scientiarum Mathematicarum Hungarica, 57(4) (December 2020), 436-443. Additional information is on the journal webpage.
  22. R. Gardner, N. K. Govil, and P. Kumar, Some Inequalities for the Maximum Modulus of Rational Functions, International Journal of Mathematics and Mathematical Sciences, Volume 2021 as Article 2263550. Additional information is on the journal webpage.
  23. R. Gardner and M. Taylor, Generalization of an Eneström-Kakeya Type Theorem to the Quaternions, Armenian Journal of Mathematics, 14(9), 1-8 (2022). Additional information is on the journal webpage.
  24. R. Gardner and M. Gladin, Generalizations of the Eneström-Kakeya Theorem Involving Weakened Hypotheses, AppliedMath, 2(4), 687-699 (2022). Additional information is on the journal webpage.
  25. R. Gardner and M. Gladin, The Number of Zeros in a Disk of a Complex Polynomial with Coefficients Satisfying Various Monotonicity Conditions, AppliedMath, 3(4), 722-729 (2023). Additional information is on the journal webpage.
Applied Probability and Statistics
  1. R. Gardner, A Statistical Analysis of Sand Grain Size in San Salvador, Bahamas, Occasional Papers of the Bahamian Field Station, 1 (1993).
  2. R. Gardner and M. Wooten, An Application of Bayes' Theorem to Population Genetics, in Logic, Probability and Science, eds. N. Shanks and R. Gardner, Poznan Studies in the Philosophy of the Sciences and the Humanities, volume 71, Rodopi, Amsterdam/Atlanta, 2000.
  3. R. Gardner, Commentary on "The Exchange Paradox, Finite Additivity, and the Principle of Dominance" by Piers Rawling, in Logic, Probability and Science, eds. N. Shanks and R. Gardner, Poznan Studies in the Philosophy of the Sciences and the Humanities, volume 71, Rodopi, Amsterdam/Atlanta, 2000.
  4. R. Gardner and R. Price, Translation Invariance and Finite Additivity in a Probability Measure on the Natural Numbers, International Journal of Mathematics and Mathematical Sciences, 29(10) (2002) 585-589 (MR#1900503).
Math and Statistics Teaching
  1. R. Gardner, A Useful Notation for Rules of Differentiation, The College Journal of Mathematics, 24(4) (1993) 351-352. Reprinted in The Calculus Collection: A Resource for AP and Beyond, pages 257-58, edited by C. Diefenderfer and R. Nelsen, The Mathematical Association of America, 2010 (ISBN: 978-0-88385-761-8). Partially available on Google books.
  2. R. Gardner, An Application of Differential Calculus to Population Genetics, Mathematics and Computer Education, 29(3) (1995) 305-311.
  3. R. Gardner, Horizontal Asymptotes: What They are Not, The Mathematics Teacher (Reader Reflections), February 1998, 152.
  4. L. Briggs, S. Brown, R. Gardner, and R. Davidson, D.RA.MA: An Extended Conceptualization of Student Anxiety in Criminal Justice Research Methods Courses, Journal of Criminal Justice Education, 20(3) (2009) 217-226.
  5. R. Davidson and R. Gardner, Hypothesis Testing Using the Films of the Three Stooges, Teaching Statistics, 32(2) (2010) 49-53.
  6. R. Gardner and R. Davidson, Mathematical Lens: The Three Stooges Meet the Conic Sections, Mathematics Teacher, 105(6) (February 2012), 414-418.
Other
  1. N. Shanks and R. Gardner, Introduction to Logic, Probability and Science, Poznan Studies in the Philosophy of the Sciences and the Humanities, pp. 9-15, volume 71, Rodopi, Amsterdam/Atlanta (2000).
Books Coauthored
  1. Real Analysis with an Introduction to Wavelets, with Don Hong and Jianzhong Wang, Academic Press/Elsevier Press, 2005 (ISBN hardcover: 9780123548610, ISBN eBook: 9780080540313). Parts of this book can be previewed at Google books. Additional details are available on the Elsevier Press website.
  2. Extremal Problems and Inequalities of Markov-Bernstein Type for Algebraic Polynomials, with Narendra K. Govil and Gradimir V. Milovanović, Elsevier Press, 2022 (ISBN: 978-0-12-811988-4). Parts of this book can be previewed at the Elsevier Press website and on Google books.
Book Coedited
  1. N. Shanks and R. Gardner, editors of Logic, Probability and Science, Poznan Studies in the Philosophy of the Sciences and the Humanities, volume 71, Rodopi, Amsterdam/Atlanta, 2000 (ISBN: 978-90-420-1253-0). Parts of this book can be previewed at Google books. Additonal details are available on the Brill publications website.
Work Submitted
  1. R. Gardner and M. Gladin, A Type of Eneström-Kakeya Theorem for Quaternionic Polynomials Involving Monotonicity with a Reversal , submitted to Annales Mathematicae Silesianae.
Theses and Dissertation
  1. On the Zeros of Polynomials and Bernstein Type Inequalities for Polynomials and Related Entire Functions, (Ph.D dissertation, Department of Algebra, Combinatorics, and Analysis) Auburn University, August 30, 1991.
  2. The Application of DNA Fingerprints to the Reconstruction of Genealogies within Populations, (M.S. Thesis, Department of Zoology and Wildlife Science) Auburn University, March 20, 1992.
  3. Automorphisms of Steiner Triple Systems, (M.S. Thesis, Department of Algebra, Combinatorics, and Analysis) Auburn University, August 1987.
Work of Kathryn Kreyenbuhl-Gardner
  1. A Sociological Analysis of Premenstrual Syndrome, ETSU Master's Thesis, Department of Sociology and Anthropology, December 2003. Also available as Electronic Theses and Dissertations, Paper 811. If you have an ETSU username and password, you can access this at http://dc.etsu.edu/etd/811.

Return to Bob Gardner's vita webpage.
Last updated: June 6, 2024.