Interests
Clifford algebras, combinatorics, probability on algebraic structures
Books
PeerReviewed Publications
 G.S. Staples. Zeon matrix inverses and the zeon combinatorial Laplacian
Adv. Appl. Clifford Algebras 31, 40 (2021).
DOI: 10.1007/s00006021011525. Read it online.
 A. Davis, G.S. Staples. Zeon and idemClifford formulations of Boolean satisfiability
Adv. Appl. Clifford Algebras 29, 60 (2019).
DOI:10.1007/s0000601909788. Read it online.
 G.S. Staples. Differential calculus of zeon functions
Adv. Appl. Clifford Algebras 29, 25 (2019).
DOI:10.1007/s0000601909436 . Read it online.
 E. Haake, G.S. Staples. Zeros of zeon polynomials and the zeon quadratic formula
Adv. Appl. Clifford Algebras 29, 21 (2019).
DOI:10.1007/s0000601909383. Read it online.
 T. Lindell, G.S. Staples. Norm inequalities in zeon algebras
Adv. Appl. Clifford Algebras 29, 13 (2019).
DOI:10.1007/s000060180934z. Read it online.
 G.S. Staples, A. Weygandt. Elementary functions and factorizations of zeons
Adv. Appl. Clifford Algebras 28, 12 (2018).
DOI: 10.1007/s0000601808360. Read it online.
 G.S. Staples. Hamiltonian cycle enumeration via fermionzeon convolution
International Journal of Theoretical Physics, 56 (2017), 39233934.
DOI:10.1007/s107730173381z. Read it online.

G.S. Staples. Zeons, orthozeons, and processes on colored graphs
Proceedings of CGI '17, Yokohama, Japan, June 2730, 2017
ACM, New York, NY, 2017.
DOI: 10.1145/3095140.3097283
 L.M. Dollar, G.S. Staples. Zeon roots
Adv. Appl. Clifford Algebras, 27 (2017), 11331145.
DOI:10.1007/s0000601607324. Read it online.
 G.S. Staples, T. Stellhorn. Zeons, orthozeons, and graph colorings
Adv. Appl. Clifford Algebras, 27 (2017), 18251845.
DOI:10.1007/s0000601607324.
Read it online.
 R. Schott, G.S. Staples. Generalized zeon algebras: theory and application to multiconstrained path problems
Adv. Appl. Clifford Algebras, 27 (2017), 4557 DOI: 10.1007/s0000601505950.
Read it online.
 A. Syarif, A. Abouaissa, L. Idoumghar, P. Lorenz, R. Schott, G.S. Staples. New Path Centrality Based on Operator Calculus Approach for Wireless Sensor Network Deployment
in IEEE Transactions on Emerging Topics in Computing. (2016).
DOI: 110.1109/TETC.2016.2585045
 G.S. Staples. Kravchuk matrices and induced operators on Clifford algebras
in Probability on Algebraic and Geometric Structures, Contemporary Mathematics, 668, Amer. Math. Soc., Providence, RI, 2016, pp. 207221.
 G.S. Staples, D. Wylie. Clifford algebra decompositions of conformal orthogonal group elements
Clifford Analysis, Clifford Algebras and Their Applications, 4 (2015), 223240. pdf
 B. Nefzi, R. Schott, Y.Q. Song, G.S. Staples, E. Tsiontsiou, An operator calculus approach for multiconstrained routing in wireless sensor networks
Proceedings of the 16th ACM International Symposium on Mobile Ad Hoc Networking and Computing, ACM, New York, 2015, 367376.
DOI: 10.1145/2746285.2746301
 C. Cassiday, G.S. Staples On representations of semigroups having hypercubelike Cayley graphs
Clifford Analysis, Clifford Algebras, and Their Applications, 4 (2015), 111130.
pdf
 J. Ben Slimane, R. Schott, YQ. Song, G.S. Staples, E. Tsiontsiou, Operator calculus algorithms for multiconstrained paths
International Journal of Mathematics and Computer Science, 10 (2015), no. 1, 69104. pdf.
 G.S. Staples, Kravchuk polynomials and induced/reduced operators on Clifford algebras
Complex Analysis and Operator Theory, 9 (2015), 445478.
DOI: 10.1007/s117850140377z.
Read it online.
 R. Schott, G.S. Staples, Operator calculus and invertible Clifford Appell systems: theory and application to the nparticle fermion algebra
Infinite Dimensional Analysis, Quantum Probability and Related Topics,
16 (2013), 1350007.
DOI: 10.1142/S0219025713500070
 G. Harris, G.S. Staples, Spinorial formulations of graph problems
Adv. Appl. Clifford Algebras, 22
(2012), 5977.
DOI: 10.1007/s0000601102980.
Read it online.
 R. Schott, G.S. Staples, Connected components and evolution of random graphs: an algebraic approach
Journal of Algebraic Combinatorics, 35 (2012), 141156.
DOI: 10.1007/s1080101102971. Read it online or
click here for the pdf.
 H. CruzSanchez, G.S. Staples, R. Schott, YQ. Song, Operator calculus approach to minimal paths: Precomputed routing in a storeandforward satellite constellation
Proceedings of IEEE Globecom, Anaheim, CA, USA, December 37, 2012, pp. 34383443.
 R. Schott, G.S. Staples, Complexity of counting cycles using zeons
Computers & Mathematics with Applications, 62 (2011), 18281837.
DOI: 10.1016/j.camwa.2011.06.026
 R. Schott, G.S. Staples, Nilpotent adjacency matrices and random graphs
Ars Combinatoria, 98 (2011), 225239.
(pdf)
 R. Schott, G.S. Staples, On the Complexity of Cycle Enumeration for Simple Graphs
in Guide to Geometric Algebra in Practice, L. Dorst and J. Lasenby (editors), Springer, 2011, pp. 233249.
DOI: 10.1007/s0000600801432
 R. Schott, G.S. Staples, Zeons, lattices of partitions, and free probability
Communications on Stochastic Analysis, 4 (2010), 311334. (pdf)
 R. Schott, G.S. Staples, Operator homology and cohomology in Clifford algebras
Cubo, A Mathematical Journal, 12 (2010), 299326.
DOI: 10.4067/S071906462010000200018
 R. Schott, G.S. Staples, Dynamic geometric graph processes: adjacency operator approach
Adv. Appl. Clifford Algebras, 20 (2010), 893921.
DOI: 10.1007/s0000601002286. Read it online.
 R. Schott, G.S. Staples, Dynamic random walks in Clifford algebras
Advances in Pure and Applied Mathematics, 1 (2010), 81115.
DOI: 10.1515/APAM.2010.007
 R. Schott, G.S. Staples, Reductions in computational complexity using Clifford algebras
Adv. Appl. Clifford Algebras, 20 (2010), 121140.
DOI: 10.1007/s0000600801432. Read it online.
 R. Schott, G.S. Staples, Computational Complexity Reductions Using Clifford Algebras
in
Geometric Algebra Computing for Engineering and Computer Science, E. BayroCorrochano and G. Scheuermann (editors), Springer Verlag, 2010, pp. 431453.
 G.S. Staples, A new adjacency matrix for finite graphs
Adv. Appl. Clifford Algebras, 18 (2008), 979991.
DOI: 10.1007/s0000600801165. Read it online.
 R. Schott, G.S. Staples, Nilpotent adjacency matrices, random graphs, and quantum random variables
Journal of Physics A: Mathematical and Theoretical, 41 (2008), 155205.
DOI: 10.1088/17518113/41/15/155205
 R. Schott, G.S. Staples, Random walks in Clifford algebras of arbitrary
signature as walks on directed hypercubes,
Markov Processes and Related Fields, 14 (2008), 515542.
 G.S. Staples, Norms and generating functions in Clifford algebras
Adv. Appl. Clifford Algebras, 18 (2008), 7592.
DOI: 10.1007/s0000600700636. Read it online.
 R. Schott, G.S. Staples, Partitions and Clifford algebras
European Journal of Combinatorics, 29 (2008), 11331138.
DOI: 10.1016/j.ejc.2007.07.003
 G.S. Staples, Graphtheoretic approach to stochastic integrals with Clifford algebras
Journal of Theoretical Probability, 20 (2007), 257274.
DOI: 10.1007/s1095900700643. Read it online.
 R. Schott, G.S. Staples, Operator calculus and Appell systems on Clifford algebras
International Journal of Pure and Applied Mathematics, 31 (2006), 427446.
 G.S. Staples, Cliffordalgebraic random walks on the hypercube
Adv. Appl. Clifford Algebras, 15 (2005), 213232.
DOI: 10.1007/s000060050014z. Read it online.
Unreviewed Publications
 R. Schott, G.S. Staples, Clifford operator calculus: homology, cohomology, and Appell systems, 9th International Conference on Clifford Algebras and their Applications in Mathematical Physics,
K. Gürlebeck (ed.),
Weimar, Germany, 1520 July 2011. pdf
 R. Schott, G.S. Staples, Clifford algebras, random graphs, and quantum random
variables, in
Quantum Stochastics and Information (Statistics, Filtering and
Control), University of Nottingham, UK, 15  22 July 2006,
V P Belavkin & M Guţă (editors), World Scientific Publishing, 2008.
Research Presentations at Conferences
 Zeon Matrix Algebra and the Zeon Combinatorial Laplacian
12th International Conference on Clifford Algebras and Their Applications (ICCA12)
Hefei, CHINA, August 37, 2020. [Online via Zoom]
 Zeon and IdemClifford Formulations of Boolean Satisfiability
ENGAGE Workshop
Computer Graphics International 2019 (CGI '19)
Calgary, CANADA, June 1720, 2019.
 Norm Inequalities in Zeon Algebras
2018 Alterman Conference and School on Geometric Algebra and Kähler Calculus (ACSGAKC 2018)
Milan, ITALY, July 2327, 2018.
 Algebraic Properties of Zeons
11th International Conference on Clifford Algebras and Their Applications (ICCA11)
Ghent, BELGIUM, August 711, 2017.
 Zeons, Orthozeons, and Processes on Colored Graphs
ENGAGE Workshop Keynote Address
Computer Graphics International 2017 (CGI '17)
Yokohama, JAPAN, June 2730, 2017.
 Traces of GraphInduced Operators on Fermions and Zeons
Quantum Structures 2016 (IQSA 2016)
Leicester, UK, 1115 July 2016.
 GraphInduced Operators on Clifford Algebras
LLMC 2016  Langenhop Lecture and SIU Mathematics Conference
Carbondale, Illinois, USA, 1617 May 2016.
 Decomposition Algorithms in Clifford Algebras
CoCoA 2015  Combinatorics and Computer Algebra
Fort Collins, Colorado, USA, 2024 July 2015.
 Operator Calculus on Clifford Algebras: Combinatorics to Quantum Probability
Invited plenary talk, 10th International Conference on Clifford Algebras and Their Applications (ICCA10)
Tartu, ESTONIA, 49 August 2014.
 Kravchuk Matrices and Induced Operators on Clifford Algebras
Probability on Algebraic and Geometric Structures
Southern Illinois University, Carbondale, Illinois, USA, 57 June 2014.
 Combinatorial Semigroups and Induced/Deduced Operators
The 4th Novi Sad Algebraic Conference & Semigroups and Applications
Novi Sad, SERBIA, June 2013.
 Operator calculus approach to minimal paths: Precomputed routing in a storeandforward satellite constellation (w. H. CruzSanchez, R. Schott, YQ. Song),
IEEE Globecom 2012, Anaheim, California, USA, December 37.
 Clifford Operator Calculus: Homology, Cohomology, and Appell Systems
Invited plenary talk, 9th International Conference on Clifford Algebras and Their Applications (ICCA9)
Weimar, GERMANY, July 2011.
 On the Complexity of Counting Cycles in Sparse Graphs using Nilpotent Adjacency Matrices
24th Midwest Conference on Combinatorics, Cryptography, and Computing
Illinois State University, Normal, Illinois, USA, September 2010.
 On the Complexity of Cycle Enumeration using Zeons
Applications of Geometric Algebras in
Computer Science and Engineering (AGACSE 2010)
Amsterdam, The NETHERLANDS, June 2010.
 GraphTheoretic Free Cumulants using Zeons
30th Conference on Quantum Probability and Related Topics
Santiago, CHILE, November 2009.
 Reductions in Computational Complexity Using Clifford Algebras
Applications of Geometric Algebras in Computer Science and Engineering (AGACSE 2008)
Leipzig, GERMANY, August 2008.
 Clifford Algebras, Graph Problems, and Computational Complexity
Invited plenary talk, 8th International Conference on Clifford Algebras and Their Applications
Campinas, BRAZIL, May 2008.
 Three Algebras Related to Random Graphs and Quantum Probability
4th International Conference of Applied Mathematics and Computing
Plovdiv, BULGARIA, August 2007.
 How Can NP Graph Problems Be Moved Into P?
20th Midwest Conference on Combinatorics, Cryptography, and Computing
Wichita State University, Wichita, Kansas, USA, October 2006.
 Clifford Algebras, Random Graphs, and Quantum Probability
27th International Conference on Quantum Probability and Infinite Dimensional Analysis
Nottingham, ENGLAND, July 2006.
 Clifford Algebras and Random Graphs
12th International Conference on Random Structures and Algorithms
Poznan, POLAND, August 2005.
 CliffordAlgebraic Generating Functions and a Frobenius Norm for Clifford Matrices
7th International Conference on Clifford Algebras and Their Applications
Toulouse, FRANCE, May 2005.
Invited Seminars & Colloquia
 Stochastic Processes on Graphs: Some Theoretical Aspects and Applications
Probability Seminar, Institut Élie Cartan, Université de Lorraine, Nancy, FRANCE, May 2012.
 Wireless Networks and Random Graphs: An Operator Calculus Approach
INRIA, Paris, FRANCE, November 2010.
 Wireless Networks and Graded Semigroup Algebras
Southern Illinois University Carbondale, November 2010.
 Wireless Networks, Random Graphs, and Clifford Algebras
Institut Élie Cartan, Université Henri PoincaréNancy I, Nancy, FRANCE, October 2010.
 Clifford Algebras, Finite Graphs, and Random Walks
Southern Illinois University Carbondale, November 2008.
 CliffordAlgebraic Generating Functions and a Frobenius Norm for Clifford Matrices
Tennessee Technological University, Cookeville, Tennessee, November 2004.
Software
Below are links to some Mathematica notebooks related to my research. I welcome comments and suggestions for improvements.
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Disclaimer: These software packages are provided "AS IS" without warranty of any kind. Should any program prove defective, the enduser assumes the cost of any necessary service, repair, or correction.
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 CLIFFMATH: Clifford algebra computations  including zeon, symClifford, and idemClifford subalgebras
Notebook (source):
Package (m. file):
Documentation
Updates:
 20190605: Revised cliffordNorm, clIdemNorm, and clSymNorm to properly allow ``pnorms'' for varying p. Previous version defaulted to p=2.
 Fermionzeon convolution examples
FermionZeonConvolution.nb
 Clifford algebra decompositions of conformal orthogonal group elements
CO_Decomposition.nb
 Zeon Roots
ZeonRoots20160722.nb
 Zeon Colorings
ZeonColorings20160721.nb
