Robert Grossman
Publications - By Topic
Hopf Algebras of Trees and Their Applications
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Robert L Grossman and Richard G. Larson, Hopf Algebras of Heap Ordered Trees
and Permutations, Communications in Algebra, 2008, to appear. Also
arxiv.org/abs/0706.1327.
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Robert L. Grossman and Richard G. Larson,
Differential Algebra Structures on Families of Trees,
Advances in Applied Mathematics, Volume 35, pages 97-119, 2005.
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Robert L. Grossman and Richard G. Larson,
Bialgebras and Realizations,
in Hopf Algebras, Jeffrey Bergen, Stefan Catoiu, and William
Chin, editors, Marcel Dekker, Inc., New York, 2004, pages 157-166.
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R. L. Grossman and R. G. Larson, An Algebraic Approach to Data
Mining: Some Examples, Proceedings of the 2002 IEEE International
Conference on Data Mining, IEEE Computer Society, Los Alamitos,
California, 2002, pages 613-616.
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R. L. Grossman and M. Sweedler Hybrid Systems
and Quantum Automata: Preliminary Announcement, Hybrid Systems
II, P. Antsaklis, W. Kohn, A. Nerode, S. Sastry, editors,
Springer Lecture Notes in Computer Science, Volume 999, pages 191-201,
1995.
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M. J. Doffou and R. L. Grossman, The Symbolic
Computation of Differential Invariants of Polynomial Vector Field
Systems Using Trees, Proceedings of the 1995 International
Symposium on Symbolic and Algebraic Computation, A. H. M. Levelt,
editor, ACM, 1995, pages 26-31.
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P. E. Crouch, R. Grossman, Y. Yan, On the numerical
integration of the rolling ball equations using geometrically
exact algorithms, Mechanics of Structures of Machines, 1994.
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P. Crouch and R. Grossman, Numerical integration
of ordinary differential equations on manifolds, Journal of
Nonlinear Science, Volume 3, pages 1-33, 1993.
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R. L. Grossman and R. L. Larson, Some Remarks
About Flows in Hybrid Systems, in R. L. Grossman, A. Nerode,
A. P. Ravn, and H. Rischel, editors, Hybrid Systems, Lecture
Notes in Computer Science, Volume 736, Springer-Verlag, New York,
1993, pp. 357-365.
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Robert L. Grossman, Symbolic Computation and Flows of Differential
Equations, Second Workshop on Computer Algebra, July 21, 1993,
Rio de Janeiro.
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R. Grossman and R. G. Larson, The realization
of input-output maps using bialgebras, Forum Mathematicum,
Volume 4, 1992, pages 109-121.
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R. Grossman and R. Larson, The symbolic computation
of derivations using labeled trees, Journal of Symbolic Computation,
Volume 13, pages 511-523, 1992.
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R. Grossman and D. Radford, A simple construction
of bialgebra deformations, Contemporary Mathematics: Quantum
Groups and Deformations, AMS, pp. 115-117, 1992.
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P.E. Crouch and R. L. Grossman, The Explicit
Computation of Integration Algorithms and First Integrals for
Ordinary Differential Equations With Polynomial Coefficients Using
Trees, Proceedings of the 1992 International Symposium on
Symbolic and Algebraic Computation, ACM Press, pp. 89-94.
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R. L. Grossman and R. G. Larson, Viewing hybrid
systems as products of control systems and automata, Proceedings
of the 31st IEEE Conference on Decision and Control, IEEE Press,
1992, pages 2953-2955.
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P.E. Crouch, R. Grossman, and Y. Yan, On the
numeric integration of dynamic attitude equations, Proceedings
of the 31st IEEE Conference on Decision and Control, IEEE Press,
1992, pages 1497-1501.
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R. Grossman, The evaluation of expressions
involving higher order derivations, Journal of Mathematical
Systems, Estimation, and Control, Volume 1, 1991, pages 91-106.
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R. Grossman, Using trees to compute approximate
solutions of ordinary differential equations exactly, Differential
Equations and Computer Algebra M. Singer, editor, Academic Press,
New York, 1991, pp. 29-59.
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P. Crouch, R. Grossman, and R. G. Larson, Computations
involving differential operators and their actions on functions,
Proceedings of 1991 International Symposium on Symbolic and
Algebraic Computation, ACM, 1991, pp. 301-307.
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R. Grossman and R. G. Larson, The symbolic
computation of vector field expressions, Algebraic Computing
in Control 1991, edited by G. Jacob and F. Lamnabhi-Lagarrigue,
Springer-Verlag, Berlin, 1991, pp. 1-10.
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Robert L. Grossman and David Radford,
Bialgebra Deformations of Certain Universal Enveloping Algebras,
Laboratory for Advanced Computing Technical Report,
University of Illinois at Chicago, 1991.
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R. Grossman and R. Larson, Hopf-algebraic structure of combinatorial
objects and differential operators, Israel Journal Mathematics, Volume 72,
1990, pages 109-117.
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M. Grayson and R. Grossman, Models for free, nilpotent Lie algebras,
Journal Algebra, Vol. 35, 1990, pages 177-191.
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R. Grossman and R. Larson, Solving nonlinear
equations from higher order derivations in linear stages, Advances
in Mathematics, Vol. 82, 1990, pages 180-202.
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R. Grossman and R. Larson, Hopf algebraic structures of families of
trees, Journal Algebra, Vol. 26, 1989, pages 184-210.
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R. Grossman and R. Larson, Labeled trees and the algebra of
differential operators, Graphs and Algorithms, Contemporary
Mathematics, Volume 89, B. Richter, editor, American Mathematical
Society, Providence, 1989, pages 81-87.
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M. Grayson and R. Grossman, Nilpotent Lie algebras
and vector fields, Symbolic Computation: Applications to Scientific
Computing, R. Grossman, editor, SIAM, Philadelphia, 1989, pages 77-96.
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R. Grossman and R. G. Larson, Labeled trees
and the efficient computation of derivations, Proceedings of
1989 International Symposium on Symbolic and Algebraic Computation,
ACM, 1989, pages 74-80.
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R. Grossman and R. Larson, The symbolic computation
of higher order derivations: symmetries of expressions and actions
of group algebras, Differential Geometry: The Interface Between
Pure and Applied Mathematics, Contemporary Mathematics, 68, M.
Luksic, C. Martin and W. Shadwick, editors, American Mathematical
Society, Providence, 1987, pages 121-131.
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