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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 (Unpublished)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 | ||||
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| Subjects: | Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software | ||||
| Divisions: | Faculty of 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: |
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| 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| Status: | Not Peer Reviewed | ||||
| Publication Status: | Unpublished | ||||
| Publisher Statement: | D.E. Daykin, J.W. Daykin and M.S. Paterson, “On Log Concavity for Order-Preserving and Order-non-Reversing Maps of Partial Orders”, <i>Discrete Mathematics</i> <b>50</b>, pp. 221-226 (1984) | ||||
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