Explore a selection of works produced by faculty in the Department of Mathematical Sciences at Michigan Technological University.

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Submissions from 2015

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Automorphisms of strongly regular graphs and PDS in Abelian groups, Zeying Wang, Stefaan DeWinter, and Ellen Kamischke

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On the number of odd values of the Klein j-function and the cubic partition function, Fabrizio Zanello

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Zeilberger's KOH theorem and the strict unimodality of q-binomial coefficients, Fabrizio Zanello

Submissions from 2014

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On the weak Lefschetz property for artinian Gorenstein algebras of codimension three, Mats Boij, Juan Migliore, Rosa Miro-Roig, Uwe Nagel, and Fabrizio Zanello

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The nonexistence of (18,3,18,6) relative difference sets, David C. Clark and Vladimir Tonchev

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Two unfortunate properties of pure f-vectors, Adrian Pastine and Fabrizio Zanello

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On the rank function of a differential poset, Richard Stanley and Fabrizio Zanello

The existence of optimal quaternary [28,20,6] and quantum [[28,12,6]] codes, Vladimir Tonchev

Submissions from 2013

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A new class of majority-logic decodable codes derived from polarity designs, David C. Clark and Vladimir Tonchev

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Enumeration of (16,4,16,4) relative difference sets, David C. Clark and Vladimir Tonchev

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An equation error approach for the elasticity imaging inverse problem for predicting tumor location, E. Crossen, Mark Gockenbach, Baasansuren Jadamba, Akhtar A. Khan, and Brian Winkler

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A direct product construction for high-rate self-synchronizing codes, Yuichiro Fujiwara and Vladimir Tonchev

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High-rate self-synchronizing codes, Yuichiro Fujiwara and Vladimir Tonchev

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Algebraic techniques in designing quantum synchronizable codes, Yuichiro Fujiwara, Vladimir Tonchev, and Tony Wong

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Local convergence of Newton’s method in the classical calculus of variations, Mark Gockenbach and Chang Liu

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Pure O-Sequences and Matroid h-Vectors, Huy Tai Ha, Erik Stokes, and Fabrizio Zanello

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New invariants for incidence structures, Dieter Jungnickel and Vladimir Tonchev

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Warnaarʼs bijection and colored partition identities, I, Colin Sandon and Fabrizio Zanello

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Warnaar’s bijection and colored partition identities, II, Colin Sandon and Fabrizio Zanello

Submissions from 2012

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Stability and error estimates for an equation error method for elliptic equations, Mohammad F. Al-Jamal and Mark Gockenbach

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Nonbinary quantum codes derived from finite geometries, David C. Clark and Vladimir Tonchev

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Pure O-sequences: Known results, applications, and open problems, Juan Migliore, Uwe Nagel, and Fabrizio Zanello

Submissions from 2011

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On the shape of a pure O -sequence, Mats Boij, Juan Migliore, Rosa Miro-Roig, Uwe Nagel, and Fabrizio Zanello

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Affine geometry designs, polarities, and Hamada's conjecture, David C. Clark, Dieter Jungnickel, and Vladimir Tonchev

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Information security, coding theory and related combinatorics, Dean Crnkovic and Vladimir Tonchev

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A Hamada type characterization of the classical geometric designs, Dieter Jungnickel and Vladimir Tonchev

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Finite geometry designs, codes, and Hamada's conjecture, Vladimir Tonchev

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The KOH terms and classes of unimodal N-modular diagrams, Fabrizio Zanello

Submissions from 2010

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Mutually disjoint designs and new 5‐designs derived from groups and codes, Makoto Araya, Masaaki Harada, Vladimir Tonchev, and Alfred Wassermann

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Some algebraic consequences of Green’s hyperplane restriction theorems, Mats Boij and Fabrizio Zanello

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Exponential bounds on the number of designs with affine parameters, David C. Clark, Dieter Jungnickel, and Vladimir Tonchev

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Entanglement-assisted quantum low-density parity-check codes, Yuichiro Fujiwara, David C. Clark, Peter Vandendriessche, Maarten De Boeck, and Vladimir Tonchev

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Finite-dimensional linear algebra, Mark Gockenbach

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Partial differential equations: Analytical and numerical methods, Second edition, Mark Gockenbach

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Classification of generalized Hadamard matrices H(6,3) and quaternary Hermitian self-dual codes of length 18, Masaaki Harada, Clement Lam, Akihiro Munemasa, and Vladimir Tonchev

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The number of designs with geometric parameters grows exponentially, Dieter Jungnickel and Vladimir Tonchev

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Monomial complete intersections, the weak Lefschetz property and plane partitions, Jizhou Li and Fabrizio Zanello

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Simplicial complexes and Macaulay’s inverse systems, Adam Van Tuyl and Fabrizio Zanello

Submissions from 2009

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Newton’s law of heating and the heat equation, Mark Gockenbach and Kristin Schmidtke

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Bounds and asymptotic minimal growth for Gorenstein Hilbert functions, Juan Migliore, Uwe Nagel, and Fabrizio Zanello

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The twisted Grassmann graph is the block graph of a design, Akihiro Munemasa and Vladimir Tonchev

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Combinatorial designs and code synchronization, Vladimir Tonchev

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Generalized weighing matrices and self-orthogonal codes, Vladimir Tonchev

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An algorithm for optimal comma free codes with isomorphism rejection, Hao Wang and Vladimir Tonchev

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Interval conjectures for level Hilbert functions, Fabrizio Zanello

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Forcing the strong Lefschetz and the maximal rank properties, Fabrizio Zanello and Jeffery Zylinski

Submissions from 2008

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Numerical analysis of elliptic inverse problems with interior data, Mark Gockenbach

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Equation error approach for elliptic inverse problems with an application to the identification of Lamé parameters, Mark Gockenbach, Baasansuren Jadamba, and Akhtar A. Khan

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An abstract framework for elliptic inverse problems: Part 2. An augmented Lagrangian approach, Mark Gockenbach and Akhtar A. Khan

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On affine designs and Hadamard designs with line spreads☆, V. C. Mavron, T. P. McDonough, and Vladimir Tonchev

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A characterization of Gorenstein Hilbert functions in codimension four with small initial degree, Juan Migliore, Uwe Nagel, and Fabrizio Zanello

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An improved multiplicity conjecture for codimension 3 Gorenstein algebras, Juan Migliore, Uwe Nagel, and Fabrizio Zanello

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On the degree two entry of a Gorenstein h-vector and a conjecture of Stanley, Juan Migliore, Uwe Nagel, and Fabrizio Zanello

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The strength of the weak Lefschetz property, Juan Migliore and Fabrizio Zanello

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Difference systems of sets and cyclotomy, Yukiyasu Mutoh and Vladimir Tonchev

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Cyclic quasi-symmetric designs and self-orthogonal codes of length 63☆, Chekad Sarami and Vladimir Tonchev

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On affine designs and GMW difference sets, Vladimir Tonchev

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Quantum codes from caps, Vladimir Tonchev

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Steiner systems for two-stage disjunctive testing, Vladimir Tonchev

Submissions from 2007

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The output least-squares approach to estimating Lamé moduli, Mark Gockenbach

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An abstract framework for elliptic inverse problems: Part 1. An output least-squares approach, Mark Gockenbach and Akhtar A. Khan

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On conflict-avoiding codes of length n=4m for the active users, Masakazu Jimbo, Miwako Mishima, Susan Janiszewski, Amin Teymorian, and Vladimir Tonchev

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An algorithm for optimal difference systems of sets, Vladimir Tonchev and Hao Wang

Submissions from 2006

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Hyperplane partitions and difference systems of sets☆, Ryoh Fuji-Hara, Akihiro Munemasa, and Vladimir Tonchev

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Understanding and implementing the finite element method, Mark Gockenbach

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Experiences in using spatial skills testing instruments with younger audiences, Sheryl Sorby, Thomas David Drummer, and Raymond E. Molzon

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A Class of 2-(3n7, 3n−1 7, (3n−1 7−1)/2) Designs, Vladimir Tonchev

Submissions from 2005

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Identification of Lamé parameters in linear elasticity: a fixed point approach, Mark Gockenbach and Akhtar A. Khan

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Symmetric (4,4)-Nets and Generalized Hadamard Matrices Over Groups of Order 4, Masaaki Harada, Clement Lam, and Vladimir Tonchev

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A characterization of designs related to an extremal doubly-even self-dual code of length 48, Masaaki Harada, Akihiro Munemasa, and Vladimir Tonchev

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Affine designs and linear orthogonal arrays☆, Vladimir Tonchev

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Partitions of difference sets and code synchronization, Vladimir Tonchev

Submissions from 2004

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A new quasi-symmetric 2-(56,16,6) design obtained from codes, Akihiro Munemasa and Vladimir Tonchev

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On generalized Hadamard matrices of minimum rank, Vladimir Tonchev

Submissions from 2003

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Unitals and codes, Anton Betten, Dieter Betten, and Vladimir Tonchev

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Adaptive simulation, the adjoint state method, and optimization, Mark Gockenbach and William W. Symes

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Self-orthogonal codes from symmetric designs with fixed-point-free automorphisms, Masaaki Harada and Vladimir Tonchev

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A formula for the number of Steiner quadruple systems on 2n points of 2‐rank 2n−n, Vladimir Tonchev

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A note on MDS codes, n-Arcs and complete designs, Vladimir Tonchev

Submissions from 2002

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A variational method for recovering planar Lamé moduli, Jun Chen and Mark Gockenbach

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Efficient and automatic implementation of the adjoint state method, Mark Gockenbach, Daniel Reynolds, Peng Shen, and William W. Symes

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Automatic differentiation and the adjoint state method, Mark Gockenbach, Daniel Reynolds, and William W. Symes

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Perfect codes and balanced generalized weighing matrices, II☆, Dieter Jungnickel and Vladimir Tonchev

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On a class of twin balanced incomplete block designs, Hadi Kharaghani and Vladimir Tonchev

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A new bound on the number of designs with classical affine parameters, Clement Lam and Vladimir Tonchev

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A Varshamov-Gilbert bound for a class of formally self-dual codes and related quantum codes, Vladimir Tonchev

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Error-correcting codes from graphs, Vladimir Tonchev

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Linear codes and the existence of a reversible Hadamard difference set inZ2×Z2×Z45☆, M. van Eupen and Vladimir Tonchev

Submissions from 2001

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A primer on differentiation, Mark Gockenbach

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The [52, 26, 10] binary self-dual codes with an automorphism of Order 7☆, W. Cary Huffman and Vladimir Tonchev

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Bush‐type Hadamard matrices and symmetric designs, Zvonimir Janko, Hadi Kharaghani, and Vladimir Tonchev

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The existence of a Bush-Type Hadamard Matrix of order 324 and two new infinite classes of symmetric designs, Zvonimir Janko, Hadi Kharaghani, and Vladimir Tonchev

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Bounds on the number of Hadamard designs of even order, Clement Lam, Sigmund Lam, and Vladimir Tonchev

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A Mass Formula for Steiner Triple Systems STS(2n−1) of 2-Rank 2n−n☆, Vladimir Tonchev

Submissions from 2000

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Maximal arcs and disjoint maximal arcs in projective planes of order 16, Nicholas Hamilton, Stoicho Stoichev, and Vladimir Tonchev

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Bounds on the number of affine, symmetric and Hadamard designs and matrices☆, Clement Lam, Sigmund Lam, and Vladimir Tonchev

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On symmetric nets and generalized Hadamard matrices from affine designs, Vassili C. Mavron and Vladimir Tonchev

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Unital designs in planes of order 16, Stoicho Stoichev and Vladimir Tonchev

Submissions from 1999

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C++ classes for linking optimization with complex simulations, Mark Gockenbach, Matthew J. Petro, and William W. Symes

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Decompositions of difference sets☆, Dieter Jungnickel and Vladimir Tonchev