MathDB
Miklos Schweitzer 1979_1

Source:

January 28, 2009
combinatorics proposedcombinatorics

Problem Statement

Let the operation f f of k k variables defined on the set {1,2,…,n} \{ 1,2,\ldots,n \} be called <spanclass=′latex−italic′>friendly</span> <span class='latex-italic'>friendly</span> toward the binary relation ρ \rho defined on the same set if f(a1,a2,…,ak)  ρ   f(b1,b2,…,bk) f(a_1,a_2,\ldots,a_k) \;\rho\ \;f(b_1,b_2,\ldots,b_k) implies ai  ρ bi a_i \; \rho \ b_i for at least one i,1≤i≤k i,1\leq i \leq k. Show that if the operation f f is friendly toward the relations "equal to" and "less than," then it is friendly toward all binary relations. B. Csakany
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