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The minimum number of chains in a noncrossing partition of a poset (2302.00874v2)
Published 2 Feb 2023 in math.CO and math.OC
Abstract: The notion of noncrossing partitions of a partially ordered set (poset) is introduced here. When the poset in question is $[n]={1,2,\dots, n}$ with the complete order of natural numbers, conventional noncrossing partitions arise. The minimum possible number of chains contained in a noncrossing partition of a poset clearly reflects the structural complexity of the poset. For the poset $[n]$, this number is just one. However, for a generic poset, it is a challenging task to determine the minimum number. Our main result in the paper is some characterization of this quantity.