MathDB

(355) 4

Part of 1992 Tournament Of Towns

Problems(1)

TOT 355 1992 Autumn A S4 permutations of mn elemens in mxn table

Source:

6/10/2024
A table has mm rows and nn columns. The following permutations of its mnmn elements are permitted: an arbitrary permutation leaving each element in the same row (a“horizontal move”) and an arbitrary permutation leaving each element in the same column (a “vertical move”). Find the number kk such that any permutation of mnmn elements can be obtained by kk permitted moves but there exists a permutation that cannot be achieved in less than kk moves.
(A Andjans, Riga0
combinatorics