Abstract
Lete(P) denote the number of linear extensions of a partial orderP. Interpreting the diagram ofP as a network, ande(P) as the value of a flow, we prove some upper and lower bounds fore(P). One of the consequences is the following. If the incomparability graph ofP can be covered by the incomparability graphs of ordersP 1,P 2,...,P k thene(P) ≤e(P 1)e(P 2)...e(P k ).
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Communicated by I. Rival
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Sidorenko, A. Inequalities for the number of linear extensions. Order 8, 331–340 (1991). https://doi.org/10.1007/BF00571183
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DOI: https://doi.org/10.1007/BF00571183