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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Rook theory. I. Rook equivalence of Ferrers boards
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by Jay R. Goldman, J. T. Joichi and Dennis E. White PDF
Proc. Amer. Math. Soc. 52 (1975), 485-492 Request permission

Abstract:

We introduce a new tool, the factorial polynomials, to study rook equivalence of Ferrers boards. We provide a set of invariants for rook equivalence as well as a very simple algorithm for deciding rook equivalence of Ferrers boards. We then count the number of Ferrers boards rook equivalent to a given Ferrers board.
References
  • Louis Comtet, Analyse combinatoire. Tomes I, II, Collection SUP: “Le Mathématicien”, 4, vol. 5, Presses Universitaires de France, Paris, 1970 (French). MR 0262087
  • Dominique Foata, Étude algébrique de certains problèmes d’analyse combinatoire et du calcul des probabilités, Publ. Inst. Statist. Univ. Paris 14 (1965), 81–241 (French). MR 220327
  • D. Foata and M. P. Schützenberger, On the rook polynomials of Ferrers relations, Combinatorial theory and its applications, II (Proc. Colloq., Balatonfüred, 1969) North-Holland, Amsterdam, 1970, pp. 413–436. MR 0360288
  • —, Théorie géométrique des polynômes eulériens, Lecture Notes in Math., vol. 138, Springer-Verlag, Berlin and New York, 1970. MR 42 #7523.
  • Solomon W. Golomb and Leonard D. Baumert, Backtrack programming, J. Assoc. Comput. Mach. 12 (1965), 516–524. MR 195585, DOI 10.1145/321296.321300
  • Donald E. Knuth, The art of computer programming. Volume 3, Addison-Wesley Series in Computer Science and Information Processing, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1973. Sorting and searching. MR 0445948
  • Ronald Mullin and Gian-Carlo Rota, On the foundations of combinatorial theory. III. Theory of binomial enumeration, Graph Theory and its Applications (Proc. Advanced Sem., Math. Research Center, Univ. of Wisconsin, Madison, Wis., 1969) Academic Press, New York, 1970, pp. 167–213 (loose errata). MR 0274300
  • John Riordan, An introduction to combinatorial analysis, Wiley Publications in Mathematical Statistics, John Wiley & Sons, Inc., New York; Chapman & Hall, Ltd., London, 1958. MR 0096594
  • Gian-Carlo Rota, The number of partitions of a set, Amer. Math. Monthly 71 (1964), 498–504. MR 161805, DOI 10.2307/2312585
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Additional Information
  • © Copyright 1975 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 52 (1975), 485-492
  • MSC: Primary 05A15
  • DOI: https://doi.org/10.1090/S0002-9939-1975-0429578-4
  • MathSciNet review: 0429578