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- Publisher
- de Gruyter
- Copyright
- Copyright © 2009 Walter de Gruyter
- ISSN
- 0924-9265
- eISSN
- 1569-3929
- DOI
- 10.1515/dma.1993.3.3.229
- Publisher site
- See Article on Publisher Site
Abstract
-- This article reviews the results obtained by native and foreign authors for the most part in the last decade, these results are interpreted hi the context of both dassical and new trends of the enumeration theory of permutations with restricted positions which is a section of combinatorial analysis founded by Euler. The material of the review is given in accordance with the author's classification of the main trends of the theory. A series of previously announced author's results, which generalize the well-known publications of West mathematicians, are presented in detail. 1. INTRODUCTION The enumeration theory of permutations with restricted positions (p.r.p.) has long been formed as an important section of combinatorial analysis. The roots of this theory go back to Euler and Montmort who gave correspondingly recurrent and explicit solutions of the famous 'probleme des rencontres' (see [1]) in the 18th century. Many problems of the theory of p.r.p. are naturally formulated in terms of permanents and their generalizations. Rapid development of the theory of permanents in recent years has a considerable effect on the progress in the enumeration theory of p.r.p. Let be a permutation of elements 1,2,..., and let be its incidence matrix. The class
Journal
Discrete Mathematics and Applications – de Gruyter
Published: Jan 1, 1993