Posets with seven linear extensions sortable by three comparisons

Authors:
Satoshi Hanamura;Shigeki Iwata
Affiliations:
Department of Computer Science, The University of Electro-Communications, Chofu-shi, Tokyo 182-8585, Japan;Department of Computer Science, The University of Electro-Communications, Chofu-shi, Tokyo 182-8585, Japan
Venue:
Information Processing Letters
Year:
2011

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Abstract

If every relation in a partial order also holds in a total order, then the total order is called linear extension of the partial order. The number of linear extensions is closely related with the number of minimum comparisons to sort the poset (D.E. Knuth, Sorting and Searching, 2nd ed., The Art of Computer Programming, Addison-Wesley, Reading, MA, 1998) [5]. We show that three comparisons suffice to sort any poset having seven linear extensions, and this result may speed up exhaustive computation to derive the lower bound of the minimum number of comparisons in sorting.