Kent E. Morrison

Combinatorics of Algebraic Structures

• Knots and ones (with E. Basor and B. Conrey), 2017.
• Integer sequences and matrices over finite fields, Journal of Integer Sequences 9 (2006) Article 06.2.1.
• How much does a matrix of rank k weigh? (with Theresa Migler and Mitchell Ogle), Mathematics Magazine 79 (2006) 262-271.
• The polynomial analogue of a theorem of Rényi, Proc. Amer. Math. Soc. 133(10) (2005) 2897-2902 (electronic).
• An introduction to q-species , Electronic Journal of Combinatorics 12(1) (2005) R 62.
• q-Exponential families, Electronic Journal of Combinatorics 11(1) (2004) R 36.
• Matrices with no eigenvalues of 0 or 1, 2004.
• The probability that random polynomials are relatively r-prime (with Zhou Dong), 2004, a more abstract version of the following paper.
• Probabilistic aspects of the integer-polynomial analogy (with Zhou Dong), 2004.
• Random polynomials over finite fields, 1999.
• Eigenvalues of random matrices over finite fields, 1999.
• A Bayseian eigenvalue game, 1999.
• Random maps and permutations, 1998, revised 2003.

Probability, Game Theory, Fair Division

• Exact probabilities for three and four dice in the balanced uniform model of 3-sided dice, 2023.
• Coexistence of many species in random ecosystems (with C. A. Serván, J. A. Capitán, J. Grilli, S. Allesina), Nature Ecology and Evolution 2 (2018) 1237-1242. (Published version, non-printing, view only)
• Intransitive dice (with B. Conrey, J. Gabbard, K. Grant, A. Liu), Mathematics Magazine 89 (2016) 133-143.
• Guessing games (with Anthony Mendes), Amer. Math. Monthly 121 (2014) 33-44.
• From bocce to positivity: some probabilistic linear algebra, Mathematics Magazine 86 (2013) 110-119.
• Optimal strategies for a game on amenable semigroups (with Valerio Capraro), International Journal of Game Theory 42 (2013) 917-929.
• The multiplication game, Mathematics Magazine 83 (2010) 100-110.
• The FedEx problem, College Mathematics Journal 41 (2010) 223-232.
• The probability that a random subspace contains a positive vector, 2010.
• Cutting cakes carefully (with T. P. Hill), College Mathematics Journal 41 (2010) 281-288.
• Scale-distortion inequalities for mantissas of finite data sets (with A. Berger and T. P. Hill), J. Theoret. Probab. 21 (2008) 97-117.
• The probability that a matrix of integers is diagonalizable (with Andrew Hetzel and Jay Liew), Amer. Math. Monthly 114 (2007) 491-499.
• Random walks with decreasing steps, 1998.
• Cosine products, Fourier transforms, and random sums, Amer. Math. Monthly 102 (1995) 716-724. (Published version from JSTOR .)

Shuffle Groups

• Perfect shuffles and affine groups (with Amanda Cohen, André Harmse, Sarah Wright), 2005.
• Groups of perfect shuffles (with Steve Medvedoff), Mathematics Magazine 60 (1987) 3-14.

Linear Algebra and Operator Theory

• The trace as an average over the unit sphere of a normed space with a 1-symmetric basis (with Tomasz Kania), Operators and Matrices 10 (2016) 731-737.
• The geometry of the higher traces, 1998 and 2010.
• A generalization of circulant matrices for non-abelian groups, 1998.
• Some analogues of circulant matrices, 1995.
• Spectral approximation of multiplication operators, New York Journal of Mathematics 1 (1995) 75-96.
• The Fisher-Hartwig conjecture and Toeplitz eigenvalues (with Estelle Basor), Linear Algebra and Its Applications 202 (1994) 129-142.
• The extended Fisher-Hartwig conjecture for symbols with multiple jump discontinuities (with Estelle Basor), Operator Theory: Advances and Applications 71 (1994) 16-28.

Connections and Symplectic Geometry

• A connection whose curvature is the Lie bracket, Journal of Generalized Lie Theory and Applications 3(4) (2009) 311-319.
• Yang-Mills connections on surfaces and representations of the path group, Proc. Amer. Math. Soc. 112 (1991) 1101-1106.
• Discrete Yang-Mills connections, Physics Letters B 233 (1989) 393-394.
• Symplectic flows on the open ball, Journal of Differential Equations 46 (1982) 59-62.
• A symplectic fixed point theorem on open manifolds (with Michael Colvin), Proc. Amer. Math. Soc. 84 (1982) 601-604.

Representation Varieties

• Connected components of representation varieties, Contemporary Mathematics 74 (1988) 255-269. (2MB scanned file)
• Geometric equivalence relations on modules, Journal of Pure and Applied Algebra 22 (1981) 165-177.
• The scheme of finite dimensional representations of an algebra, Pacific Journal of Mathematics 91 (1980) 199-218. (2MB scanned file)

Dynamical Systems

• A laboratory-based nonlinear dynamics course for science and engineering students (with N. Sungar, J. P. Sharpe, M. J. Moelter, N. Fleishon, J. McDill, R. Schoonover), American Journal of Physics 69 (2001) 591-597.