Abstract
Let [n] = {1, 2, …, n}. Suppose we have k linear orderings on [n], say <1, <2, …, <k. Let M ⊆ [n]. Then M has a minimum for each linear ordering <i. So M has at most k minima. A set M ⊆ [n] is called a 2min-set if it has at most two different minima in the linear orderings <1, <2, …, <k. Similarly, a set N ⊆ [n] can have at most k minima and k maxima for any k linear orderings. A set N ⊆ [n] is called a 2minmax-set if there exist a, b ∈ N such that all the elements in N | {a, b} lie in between a and b for every linear ordering <i. In this paper, we shall determine the sizes of 2min-sets and 2minmax-sets for certain k linear orderings.
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Communicated by Imre Bárány
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Wong, K.B. On 2min-sets and 2minmax-sets with respect to certain cycles. Period Math Hung 67, 133–142 (2013). https://doi.org/10.1007/s10998-013-6670-1
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DOI: https://doi.org/10.1007/s10998-013-6670-1