On properties of multi-dimensional statistical tables

Beck, M., Pixton, D., 2002. The Ehrhart polynomial of the Birkoff polytope. Manuscript dated February 25, 2002, 14pp. Available: http://front.math.ucdavis.edu/math.CO/0202267. Beck, M., Cohen, M., Cuomo, J., Gribelyuk, P., 2002. The number of “magic” squares and hypercubes. Manuscript dated May 27, 2002. 11pp. Available: http://front.math.ucdavis.edu/math.CO/0201013. Bishop, 1975 Buzzigoli, L., Guisti, A., 1999. An algorithm to calculate the lower and upper bounds of elements of an array given its marginals. Statistical Data Protection: Proceedings of the Conference, EUROSTAT, Luxembourg, pp. 131–147. Causey, 1985, Applications of transportation theory to statistical problems, J. Amer. Statist. Assoc., 80, 903, 10.2307/2288551 Cox, 1987, A constructive procedure for unbiased controlled rounding, J. Amer. Statist. Assoc., 82, 520, 10.2307/2289455 Cox, L.H., 1999. Some remarks on research directions in statistical data protection. Statistical Data Protection: Proceedings of the Conference, EUROSTAT, Luxembourg, pp. 163–176. Cox, L.H., 2002. Bounds on entries in 3-dimensional contingency tables. Inference Control in Statistical Databases-From Theory to Practice, Lecture Notes in Computer Science, Vol. 2316. Springer, New York, pp. 21–33. Cox, 1982, Controlled rounding, INFOR, 20, 423 Cox, L.H., Fagan, J., Greenberg, B., Hemmig, R., 1986. Research at the Census Bureau into disclosure avoidance techniques for tabular data. Proceedings of the Survey Research Methods Section, American Statistical Association, Alexandria, VA, pp. 388–393. de Loera, J., Onn, S., 2002. On the complexity of three-way statistical tables. Manuscript dated, July 30, 2002. Available: http://front.math.ucdavis.edu/math.CO/0207200. Deming, 1940, On a least squares adjustment of a sampled frequency table with the expected marginals are known, Ann. Math. Statist., 11, 427, 10.1214/aoms/1177731829 Diaconis, 1998, Algebraic algorithms for sampling from conditional distributions, Ann. Statist., 26, 363, 10.1214/aos/1030563990 Ernst, L.R., 1989. Further applications of linear programming to sampling problems. Technical Report-Census/SRD/RR-89-05. Statistical Research Division, Washington, DC, US Census Bureau, 33pp. Available: http://www.census.gov/srd/papers/pdf/rr89-05.pdf. Gusfield, 1988, A graph theoretic approach to statistical data security, SIAM J. Computing, 17, 552, 10.1137/0217034 Kennington, 1980 Nemhauser, 1988 Sturmfels, 1996 US Department of Commerce, 1994. Statistical Policy Working Paper 22: Report on Statistical Disclosure Limitation Methodology. US Department of Commerce, Washington, DC (NTIS Document Sales, PB94-165305).