Abstract:
We sketch the circle of fundamental ideas and trends in the development of one of the important branches of combinatorial analysis—the theory of enumerating the permutations with restricted positions, which dates back to Euler, Monmort, Lucas, Cayley, and other classical authors. We devote a great deal of attention to new and up-to-date trends of the theory, some of which are still in the formative stage. We state 10 conjectures and problems.
Citation:
V. S. Shevelev, “Some problems of the theory of enumerating the permutations with restricted positions”, Itogi Nauki i Tekhniki. Ser. Teor. Veroyatn. Mat. Stat. Teor. Kibern., 30, VINITI, Moscow, 1992, 113–177; J. Soviet Math., 61:4 (1992), 2272–2317
\Bibitem{She92}
\by V.~S.~Shevelev
\paper Some problems of the theory of enumerating the permutations with restricted positions
\serial Itogi Nauki i Tekhniki. Ser. Teor. Veroyatn. Mat. Stat. Teor. Kibern.
\yr 1992
\vol 30
\pages 113--177
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/intv81}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1172614}
\zmath{https://zbmath.org/?q=an:0808.05002}
\transl
\jour J. Soviet Math.
\yr 1992
\vol 61
\issue 4
\pages 2272--2317
\crossref{https://doi.org/10.1007/BF01104103}
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https://www.mathnet.ru/eng/intv81
https://www.mathnet.ru/eng/intv/v30/p113
This publication is cited in the following 4 articles:
Peter Kagey, “Ranking and unranking restricted permutations”, Discrete Applied Mathematics, 355 (2024), 247
D. B. Efimov, “Enumeration of even and odd chord diagrams”, J. Appl. Industr. Math., 18:2 (2024), 216–226
D.B. Efimov, “On the permanent of multidimensional matrices”, Proceedings of the Komi Science Centre of the Ural Division of the Russian Academy of Sciences, 2024, no. 5, 11
D. B. Efimov, “On Some Properties of the Permanent of Matrices of Small Orders”, Math. Notes, 114:2 (2023), 223–229
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