منابع مشابه
Odd permutations are nicer than even ones
We give simple combinatorial proofs of some formulas for the number of factorizations of permutations in Sn as a product of two n-cycles, or of an n-cycle and an (n − 1)-cycle. © 2012 Elsevier Ltd. All rights reserved.
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Aliphatic polyamides derived from odd diamine or odd dicarboxylic acid units cannot adopt a conventional sheet structure when molecular chains have an all trans conformation. However, typical fiber diffraction patterns of this sheet structure were observed in several polyamides derived from odd units such as nylons 65 and 56. Consequently, a new structure based on the establishment of intermole...
متن کاملA note on the total number of cycles of even and odd permutations
We prove bijectively that the total number of cycles of all even permutations of [n] = {1, 2, . . . , n} and the total number of cycles of all odd permutations of [n] differ by (−1)(n − 2)!, which was proposed by Miklós Bóna. We also prove bijectively the following more general identity: n
متن کاملCounting Even and Odd Partitions
1. Introduction. It is a lovely fact that n] = f1; 2; : : : ; ng, n 1, has as many subsets X with an even cardinality jXj as those with an odd cardinality, namely 2 n?1 of both. To prove it, pair every subset X with X 1 where X 1 is Xnf1g if 1 2 X and X f1g if 1 6 2 X. Then X 7 ! X 1 is an involution that changes the parity of jXj and the result follows. More generally, in enumerative combinato...
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In this paper we examine fluctuation and frequency of the governing equation ofoscillator with odd and even nonlinearities without damping and we present a new efficientmodification of the He’s homotopy perturbation method for this equation. We applied standard andmodified homotopy perturbation method and compare them with the numerical solution (NS), also weapplied He’s Energy balance method (...
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ژورنال
عنوان ژورنال: Canadian Mathematical Bulletin
سال: 1960
ISSN: 0008-4395,1496-4287
DOI: 10.4153/cmb-1960-023-1