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On log concavity for order-preserving and order-non-reversing maps of partial orders

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Daykin, D. E., Daykin, J. W. and Paterson, Michael S. (1983) On log concavity for order-preserving and order-non-reversing maps of partial orders. Coventry, UK: University of Warwick. Department of Computer Science. (Department of Computer Science Research Report). (Unpublished)

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Abstract

Stanley used the Aleksandrov-Fenchel inequalities from the theory of nixed volumes to prove the following result. Let P be a partially ordered set with n elements, and let x ∊ P. If Ni* is the number of linear extensions , ⋋ : P + (1 , 2,...,n) satisfying ⋋ (x) = i, then the sequence N*1,…,N*n is log concave (and therefore unimodal). Here the analogous results for both order-preserving and order-non-reversing maps are proved using an explicit injection. Further, if vc is the number of order-preserving maps of P into a chain of length c, then vc is shown to be 1-og concave, and the corresponding result is established for order-non-reversing maps.

Item Type: Report
Subjects: Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software
Divisions: Faculty of Science, Engineering and Medicine > Science > Computer Science
Library of Congress Subject Headings (LCSH): Partially ordered sets
Series Name: Department of Computer Science Research Report
Publisher: University of Warwick. Department of Computer Science
Place of Publication: Coventry, UK
Official Date: May 1983
Dates:
DateEvent
May 1983Completion
Number: Number 51
Number of Pages: 9
DOI: CS-RR-051
Institution: University of Warwick
Theses Department: Department of Computer Science
Status: Not Peer Reviewed
Publication Status: Unpublished
Reuse Statement (publisher, data, author rights): D.E.&nbsp;Daykin, J.W.&nbsp;Daykin and M.S.&nbsp;Paterson, &ldquo;On Log Concavity for Order-Preserving and Order-non-Reversing Maps of Partial Orders&rdquo;, <i>Discrete Mathematics</i> <b>50</b>, pp.&nbsp;221-226 (1984)
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