Abstract
Carlitz considered in [5] \(r \times n\) matrices with entries being zero or one and the number of changes, i.e., the number of (horizontally or vertically) adjacent entries which are different. We extend these results in many ways. For instance, we exhibit that the limiting distribution is Gaussian and get explicit formulæ for some moments even in the general instance of d dimensions (instead of just two).
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References
R. J. Baxter, Exactly Solved Models in Statistical Mechanics, Academic Press, 1982.
E. A. Bender, Central and local limit theorems applied to asymptotics enumeration, Journal of Combinatorial Theory, Series A, 15 (1973), 91–111.
P. Billingsley, Convergence of Probability Measures, Wiley, 1968.
S. L. Campbell and C. D. Meyer, Generalized Inverse of Linear Transformations, Pitman, 1979.
L. Carlitz, Rectangular arrays of zeros and ones, Duke Mathematical Journal 39 (1972), 153–164.
J. M. Dufour, M. Hallin and I. Mizera, Generalized runs tests for heteroscedastic time series. Nonparametric Statistics 9 (1998), 39–86.
J. G. Kemeny, J. L. Snell and A. W. Knapp, Denumerable Markov Chains. Van Nostrand, 1966.
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Louchard, G., Prodinger, H. Random 0-1 rectangular matrices: a probabilistic analysis. Periodica Mathematica Hungarica 47, 169–193 (2003). https://doi.org/10.1023/B:MAHU.0000010819.92663.e1
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DOI: https://doi.org/10.1023/B:MAHU.0000010819.92663.e1