制限付き占有問題の簡単な計数公式

概要

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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.
日本応用数理学会の論文
1997-12-15