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Inequalities for the number of monotonic functions of partial orders
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Daykin, J. W. (1984) Inequalities for the number of monotonic functions of partial orders. Coventry, UK: University of Warwick. Department of Computer Science. (Department of Computer Science Research Report). (Unpublished)
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Abstract
Let P be a finite poset and let x,y c P. Let C be a chain. Define N(i,j) to be the number of strict order-preserving maps w : P → C satisfying w(x) = i and w(y) = j. Various inequalities are proved, commencing with Theorem 3. If r,s,t,u,v,w are non-negative integers then N(r, u+v+w)N(r+s+t, u) ≤ ( N(r+t, u+v)N(r+s, u+w). The case v = w = 0 is a theorem of Daykin, Daykin and Paterson, which is an analogue of a theorem of Stanley for linear extensions.
| Item Type: | Report | ||||
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| 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, Inequalities (Mathematics) | ||||
| Series Name: | Department of Computer Science Research Report | ||||
| Publisher: | University of Warwick. Department of Computer Science | ||||
| Place of Publication: | Coventry, UK | ||||
| Official Date: | March 1984 | ||||
| Dates: |
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| Number: | Number 65 | ||||
| Number of Pages: | 20 | ||||
| DOI: | CS-RR-065 | ||||
| Institution: | University of Warwick | ||||
| Theses Department: | Department of Computer Science | ||||
| Status: | Not Peer Reviewed | ||||
| Publication Status: | Unpublished | ||||
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