Positions Held




Research and Publications




Recognitions and Miscellany 



Incipit, Art meets mathematics in the Fourth dimension
by Stephen Lipscomb



Art meets Mathematics in the Fourth Dimension - 2nd edition published by Springer
by Stephen Lipscomb


Fractals and Universal Spaces in Dimension Theory Series: (Springer Monographs in Mathematics)
by Stephen Lipscomb


Editor of Duvall Football: Winning a National Championship (Paperback)
by Deacon Duvall



Symmetric Inverse Semigroups (Mathematical Surveys and Monographs, No 46)
by Stephen Lipscomb


My Best Friend Harley (Paperback)
by Stephen Lipscomb (Author) and John Shaw (Illustrator)


A Universal One-Dimensional Metric Space, in TOPO 72, General Topology and Its Applications (Lecture Notes in Mathematics Vol. 378), Springer-Verlag, 248—257

Imbedding One-dimensional Metric Spaces, Ph.D. Dissertation, University of Virginia, 1973
The MK 2 MOD 6 SINS Error Covariances, Naval Weapons Lab report TN-K-13-74
On Imbedding Finite-dimensional Metric Spaces, Transactions of the American Mathematical Society, 211, 1975, 143—160
An Accuracy Check of the Vertical Deflection Computations Performed in Fire Control NSWC-DL report TN-DK-29-75
With Oscar T. Schultz, An Application of the Gravity Meter Aboard Operational Submarines --- The Gravity Fix, NSWC-DL report, TR-3296, 1975
On Planar Graphs, Abstract appeared in the Topology Section of Notices of the AMS, Vol. 23, Number 1, page A-24, 1976
On the Status of Application of Representing Functions of Several Variables in Terms of Functions of One Variable and Addition, NSWC-DL, report TN-DK-29-76
An Imbedding Theorem for Metric Spaces, Proceedings of the American Mathematical Society 55, 1, 1976, 165—169
The Seven-State Filter and MK 2 MOD 6 SINS Error Covariances NSWC-DL report TN-K-8-78
Validation of the Deterministic Navigation Simulation for the Improved Accuracy Program, NSWC-DL report TR80-242
With William Farr, On Testing Sequences for Markov Characteristics, NSWC-DL TR80-462
Aids for Managing Teams that Validate Computer Simulations, 1981 Proceedings of Summer Computer Simulation Conference, sponsored by IEEE AFIPS Press, Arlington VA. 542—544
Modeling Instrument and Environmental Noise in Simulations of Inertial Navigation Systems NSWC-DL report TR-81-198
Validation and Verification Plan for the NSWC C4 6D Trajectory Model, NSWC-DL report TN82-13
On the Efficiency of the Localnet 20 Network, NSWC-DL report, 1983
A Group of a Graph and Harary Reconstructions, AMS Notices (Abstracts) 6, 1985, issue 36, page 6
Isomorphisms and Independent Sets of Graphs, AMS Notices (Abstracts), 6, June 1985, issue 38, page 253
Graph Manifolds, Reconstruction, and Inverse Semigroups, 1986, (unpublished)
Cyclic Subsemigroups of Symmetric Inverse Semigroups, Semigroup Forum, 34, 1986, 243-248
With Allen Schwenk, Problem E 3187, American Mathematical Monthly, 94 number 1, 1987, page 72, (Solved by D. West, 96 No. 1, 1989, page 60)
The Structure of The Centralizer of a Permutation, Semigroup Forum, 37 No. 3,1988, 301-312
Hypomorphic Mapping Sets in Graph Reconstruction, 1988, unpublished
Pseudosimilar Vertices and the L-group, 1988, unpublished
With Allen D. Parks, Homology And Acyclicity of Hypergraphs: A Combinatorial Invariant For Hypergraphs, NAVSWC TR 91-323
The Alternating Semigroup: Congruences and Generators, Semigroup Forum 44, 1992, 96-106
Centralizers In Symmetric Inverse Semigroups: Structure and Order, Semigroup Forum 44, 1992, 347-355
Centralizers In Symmetric Inverse Semigroups:  Structure and Order, Semigroup Order, Semigroup Forum 44, 1992, 347-355
Problems And Applications of Finite Inverse Semigroups, in Book Proceedings of the International Colloquium on Words, Languages, and Combinatorics (Kyoto Japan 28 -- 31 August 1990) Editor M. Ito, World Scientific publishing Co. Pte. lte. , Hong Kong, New Jersey, 1992
Presentations of Alternating Semigroups, Semigroup Forum 45, 1992, 249-260

With James C. Perry, Lipscomb's L(A) Space Fractalized in Hilbert's $ell^2(A)$ Space, Proceedings of the American Mathematical Society 115, No. 4, Aug. 1992, 1157-1166


With Janusz Konieczny,  Classification of $S_n$--normal Semigroups, Semigroup Forum 51,  No. 1, Jul./Aug. 1995,  73-86


With C. Dupilka, Inverse Semigroups and Boolean Matrices,  NSWCDD/MP - 95/162


With Janusz Konieczny,  Path notation for Partial Transformations,  Proceedings of the International Conference `Semigroups with Applications, Including Semigroup Rings,'St. Petersburg University of Technology, St. Petersburg, 1999, 95-102


With J. Konieczny, Centralizers in the Semigroup of Partial Transformations,  Mathematica Japonica  43 No. 3, 1998


With Janusz Konieczny, Centralizers of Permutations in the Partial Transformation  Semigroup,  Pure Mathematics and Applications  6 No. 4 yr 1995  349-354


The Infinite Alternating Semigroup,  Semigroup Forum  55 No. 1, 1997,  118-130


Digital Images and Semigroup Structures, technical paper as required for  NSWC contract March 1999


Change-of-Coordinates Semigroups I (unpublished)


With Charles Cohen, The triangle of equally-spaced Points on Spheres , December 2002 (unpublished).


With James C. Perry, The Generalization of Sierpinski’s Triangle That Lives in 4-space, Huston Journal of Mathematics, Vol. 29, No. 3, 2003, 691-709.


With J. Konieczny, The Class Equation and Counting in Factorizable Monoids, Proceedings of the AMS, Vol. 131, No. 11, Nov. 2003, 3345-3351


A minimal extension of the iterated function system for Sierpinski's gasket to one whose attractor is the 2-simplex, Houston Journal of Mathematics, Volume 31, No. 4, 2005.


The Sierpinski cheese iterated function system extended to a 3-simplex system , Houston Journal of Mathematics, Volume 33, No. 1, 2007, 169—207.


With L. Lehman and J. Konieczny, Balanced subgroups of symmetric groups , JP Jour. of Algebra, Number Theory & Appl., Vol. 5(2), 2005, 307--329.


Counting orbits of certain category actions , article in preparation 2004.


Matrix Structural Analysis of 4-web Level-0 , unpublished November 2004.


(BOOK) Symmetric Inverse Semigroups, Volume 46 in the American Mathematical Society Surveys and Monographs Series, American Mathematical Society, 166 pages, 1996. 


(BOOK) My Best Friend Harley, ISBN 1599754428, 70 pages and 88 pictures, February 2006. 


(BOOK)Editor of Duvall Football – Winning a National Championship, ISBN 0-87012-744-8, Printed by McClain Printing, Parsons, WV, 2007.


(BOOK) Fractals and Universal Spaces in Dimension Theory, in Springer’s Monographs in Mathematics Series, Springer, 246 pages, ISBN 978-0-387-85493-9, 2009.