Abstract
Some functions defined on the set of integer triangular matrices and their modifications are considered. These functions are analogs of the classical determinant and permanent functions and provide a powerful apparatus for studying sequences generated by linear recursive equations. Modifications of these functions are used to solve the problem about trajectories on Ferre diagrams and to establish new combinatorial identities.
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REFERENCES
R. A. Zatorskii [Zators'kii], “Paradeterminants and parapermanents of triangular matrices,” in: Mathematical Investigations. Proceedings of the Lvov Mathematical Society [in Ukrainian], vol. 17, no. 1, Lviv Mat. Tov., Lvov, 2002, pp. 45-54.
R. L. Graham, D. E. Knuth, and O. Patashnik, Concrete Mathematics: A Foundation for Computer Science, Addison-Wesley, Amsterdam, 1994.
I. Macdonald, Symmetric Functions and Hall Polynomials, Clarendon Press, Oxford, 1983.
G. E. Andrews, The Theory of Partitions, Addison-Wesley, Reading (Mass.), 1976.
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Zatorskii, R.A. Determinants of Triangular Matrices and Trajectories on Ferre Diagrams. Mathematical Notes 72, 768–783 (2002). https://doi.org/10.1023/A:1021433728200
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DOI: https://doi.org/10.1023/A:1021433728200