Join me at the OEIS 100K E-Party
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Notes on Uninodal Nets (scanned in Word document)
Like almost everyone whose Erdös Number is not 0 or 1, my Erdös Number is 2. Members of our faculty with Erdös Number 1 are: Al Goodman, Vilmos Totik, and Stephen Suen.
MATH LINKS OF INTEREST:
Favorite Mathematical Constants by Steven Finch
Words of Encouragement from Professor Mark Sapir
Students who have trouble understanding mathematics may take comfort in the following remark of John von Neuman:
"In mathematics you don't understand things. You just get used to them."
If you are a students and do not feel sufficiently challenged your courses try solving the Discrete Problem of the Week or one of the Seven Mathematics Problems of the Millennium.
Mathematics in fiction, music and other offbeat links:
Which Mathematical Structure is Isomorphic to our Universe? by Max Tegmark
Mathematics in Fiction and Movies Compiled by Alex Kasman
Advance answers to all my exam questions are not available here
John Bray's enlightening view of infinity
The natural numbers start with 2 by Jan Willem Nienhuys'
How to make 1 orange into 2 oranges of the same size. (aka Banach-Tarski Paradox)
Help yourself to the postscript file or pdf file of my book ELEMENTARY ABSTRACT ALGEBRA. Also you may have the latex file in case you want to revise it to suit your own taste. I ask only that you acknowledge the source and make no commercial use of it. . This version is one-sided, but may be converted to two-sided by the appropriate printer or by a photocopy machine.
Help yourself to the postscript file or pdf file of my book ELEMENTARY NUMBER THEORY. Also you may have the latex file in case you want to revise it to suit your own taste. I ask only that you acknowledge the source and make no commercial use of it. This version is one-sided, but may be converted to two-sided by the appropriate printer or by a photocopy machine. The following Maple worksheets were used also when I taught the course:
Open Questions worksheet#1 worksheet#2 worksheet#3 worksheet#4
(To use these worksheets you must have a copy of Maple on your computer. Maple x for x >= 7 should work.)
POSTSCRIPT or PDF COPIES OF RECENT ARTICLES. For papers that have already been published, the versions available here are those of the early preprints, and do not contain corrections made in the editing process, notes added in proof, etc.
The Integer Sequence Transform a↦>b where b_n is the Number of Real Roots of the Polynomial a_0+a_1x+a_2x^2+⋯+a_n x^n , with Mark Shattuck, (https://arxiv.org/abs/2107.05572J)
Computation of Quandle 2-Cocycle Knot Invariants Without Explicit 2-Cocycles , with Masahico Saito and Larry Dunning, Journal of Knot Theory and Its Ramifications 26 (2017)
Longitudinal Mapping Knot Invariant for SU(2), with Masahico Saito, Journal of Knot Theory and Its Ramifications, Vol. 27, No. 11, 1843014 (2018)
Quandle coloring and cocycle invariants of composite knots and abelian extensions, with Masahico Saito and Leandro Vendramin, J. of Knot Theory & Its Ramifications, 1650024 (2016) [34 pages]
Algebraic Properties of Quandle Extensions and Values of Cocycle Knot Invariants, with Masahico Saito, J. Knot Theory & Is Ramifications, Vol. 25, No. 14 (2016).
Quandle Coloring of Knots and Applications, with Mohamed Elhamdadi, Masahico Saito and Timothy Yeatman, J. of Knot Theory & Its Ramifications, 23, 1450035 (2014) [29 pages] DOI: 10.1142/S0218216514500357.
Connected Quandles Associated with Pointed Abelian Groups, with Mohamed Elhamdadi, Xiang-dong Hou, Masahico Saito and Timothy Yeatman,Pacific J. of Math. 264-1 (2013), 31--60.
Galkin Quandles, Pointed Abelian Groups, and Sequence A000712, with Xiang-dong Hou, Electronic Journal of Combinatorics, Volume 20, Issue 1 (2013).
Crystal Engineering using a Turtlebug Algorithm, a de novo approach to the design of binoday metal-organic frameworks, with G. McColm, M. Eddaoudi, L. Wojtas and M.Zaworotko, Crystal Growth & Design, 16 August 2011 (Communication), DOI 10/1021/cg200172j.
On Ideal Extensions of Ideal Complements, with Tom McKinley and Boris Shekhtman, Journal of Commutative Algebra, Volume 3, Number 3, Fall 2011.
The Affinity of a Permutation of a Finite Vector Space, with Xiang-dong Hou and Alec Mihailovs, Finite Fields and Their Applications, Volume 13, Issue 1, January 2007, 80-112.Volume
Tight Upper Bounds for the Domination Numbers of Graphs with Given Order and Minimum Degree, II, with Larry Dunning and Stephen Suen, Electronic Journal of Combinatorics, Volume 7 (1), 2000, R58
Inequalities Involving Gamma and Psi Functions , with Mourad Ismail, Analysis and Applications, Volume 1, Number 1, January 2003, 129--140.
Application of Upper and Lower Bounds for the Domination Number to Vizing's Conjecture, with Mourad Ismail and Stephen Suen, Ars Combinatoria 69 (2003), 97-108
On the Probability that a t-Subset of a Finite Vector Space Contains an r-Subspace---With Applications to Short, Light Codewords in a BCH Code , with Stephen Suen, Congressus Numerantium 137 (1999), 139--159
An Application of Spanning Trees to k-Point Separating Families of Functions, with Greg McColm and Boris Shekhtman, J. London Math. Soc. (2) 58 (1998), no. 2, 297-- 310.
Upperbounds of the Domination Number of a Graph, with David Fisher, Boris Shekhtman and Stephen Suen, Congressus Numerantium, 132 (1998), pp. 99-123.
Tight Upper Bounds for the Domination Numbers of Graphs with Given Order and Minimum Degree, with Larry A. Dunning, Electronic Journal of Combinatorics 4 (1997), no. 1, Research Paper 26, pp. 1--25
Domination Numbers of q-Analogues of Kneser Graphs, with Boris Shekhtman, Bulletin of the Inst. of Comb. and its Applications, Volume 19 (1997), pp. 83-92
Covering by Complements of Subspaces, II. with Boris Shekhtman, Proc. Amer. Math. Soc.125 (1997), no. 1, 251--254.
Covering by Complements of Subspaces, with Boris Shekhtman, Linear and Multilin. Algebra, Vol 49,1995, pp. 1--13.
Binomial and q-Binomial Coefficient Inequalities Related to the Hamiltonicity of the Kneser Graphs and Their q-Analogues, with Mourad Ismail, J. Comb. Theory (Series A),Vol. 76, No. 1, Oct. 1997, pp. 83--98
Separating Sets with Parallel Classes of Hyperplanes, Bulletin of the Inst. of Comb. and its Applications, Vol. 13 (1995) , 65-82.
Domination Numbers of Complete Grid Graphs, I, with Tony Yu Chang and Eleanor O. Hare, Ars Combinatoria 38 (1994), pp. 97-111.
The Domination Numbers of the 5xn and 6xn Grid Graphs, with Tony Yu Chang , Journal of Graph Theory, Vol. 17, No. 1, 81-107 (1993). Tony Yu Chang's Dissertation 1992 (For a proof of Chang's Conjecture see The Domination Number of Grids (2011), by Daniel Gonçalves, Alexandre Pinlou, Michael Rao and Stéphan Thomassé.)
Matching Subspaces with Complements in Finite Vector Spaces, Bulletin of the ICA, Vol. 6 (1992) , 33-38.
My CV Including older publications going back to 1965