Non-sexist solution of the m'enage problem (1986) [2 citations — 1 self]
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Abstract:
The m'enage problem asks for the number of ways of seating n couples at a circular table, with men and women alternating, so that no one sits next to his or her partner. We present a straight-forward solution to this problem. What distinguishes our approach is that we do not seat the ladies first. 1 The m'enage problem The m'enage problem (probl`eme des m'enages) asks for the number M n of ways of seating n man-woman couples at a circular table, with men and women alternating, so that no one sits next to his or her partner. This famous problem was initially posed by Lucas [8] in 1891, though an equivalent problem had been raised earlier by Tait [12] in connection with his work on knot theory (see Kaplansky and Riordan [6]). This problem has been discussed by numerous authors (see the references listed in [6]), and many solutions have been found. Most of these solutions tell how to compute
Citations
| 149 | An Introduction to Combinatorial Analysis – Riordan - 1958 |
| 48 | Dimer statistics and phase transitions – Kasteleyn - 1963 |
| 45 | An enumeration of knots and links, and some of their algebraic properties – Conway - 1970 |
| 18 | Statistical mechanics of dimers on a plane lattice – Fisher - 1961 |
| 17 | Combinatorial Mathematics – Ryser - 1963 |
| 7 | Théorie des Nombres – Lucas - 1961 |
| 7 | What is an answer – Wilf - 1982 |
| 6 | Solution of the ‘Problème des ménages – Kaplansky - 1943 |
| 2 | The dinner table problem – Aspvall, Liang - 1980 |
| 2 | The probability that neighbors remain neighbors after random rearrangements – Robbins - 1980 |
| 1 | Knots and classes of m'enage permutations – Gilbert - 1956 |
| 1 | On knots, i, ii, iii – Tait |
| 1 | Sur un probl`eme des permutations – Touchard - 1934 |
