Counting Formulae for the Number of Permutations with Constraints
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- Li LEI
- Ymaguchi University
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- TOMODA TOSHIAKI
- Aomori University
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- MIDORIKAWA SHOICHI
- Aomori University
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- HORIBATA TAKATOSHI
- Aomori University
Bibliographic Information
- Other Title
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- 制限付き占有問題の簡単な計数公式
- セイゲン ツキ センユウ モンダイ ノ カンタン ナ ケイスウ コウシキ
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Abstract
In this paper, we consider the following counting for the permutation problems (0≥κ≥n) : P=(1 2 3 ... n a_1 a_2 a_3 ... a_n), where a_i ≐̸i, i+, ..., i+κ-1, (mod n). When κ=1 and κ =2, this problem becomes de Montmort's Encounter Problem and Lucas's Manager Problem, respectively, and their counting formulae have been known. But when κ≥3, we have not found any easy counting formulae yet. This paper presents the following easy counting formula for κ=n-4.D^<(N-4)>_n=6・C_n-4・C_<n-1>-2・C_<n-2>+2, n≥4, where C_1=1, C_2=2, C_3=4, C_m=C_<m-1>+C_<m-2>+C_<m-3> m≥4.
Journal
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- Transactions of the Japan Society for Industrial and Applied Mathematics
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Transactions of the Japan Society for Industrial and Applied Mathematics 7 (4), 321-331, 1997
The Japan Society for Industrial and Applied Mathematics
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Details 詳細情報について
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- CRID
- 1390001205767704832
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- NII Article ID
- 110001883663
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- NII Book ID
- AN10367166
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- ISSN
- 09172246
- 24240982
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- NDL BIB ID
- 4365336
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- Text Lang
- ja
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- Data Source
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- JaLC
- NDL
- CiNii Articles
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- Abstract License Flag
- Disallowed