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Interval number of special posets and random posets

Tom Madej, Douglas B. West
1995 Discrete Mathematics  
random posets).  ...  Finally,t he fraction of the n-element posets having interval number between (1 − ε ) n 8lgn and (3/2)(  n lgn − lglgn  + 1) approaches 1 as n → ∞ (i.e., this involves the Kleitman-Rothschild model of  ...  In Section 3, we study the interval number of large posets in terms of their size, for bipartite posets and for random posets. Bipartite posets are those whose comparability graph is bipartite.  ... 
doi:10.1016/0012-365x(94)00287-s fatcat:qrdq6aqocfc6vc5mz34hx5buwm

Page 4574 of Mathematical Reviews Vol. , Issue 96h [page]

1996 Mathematical Reviews  
special posets and random posets.  ...  Finally, the fraction of the n-element posets having interval number between (1 —«)n/8lgn and (3/2)([n/(lgn —lglgm)] +1) approaches 1 as n — oo (using the Kleitman-Rothschild model of random posets).”  ... 

Limits of interval orders and semiorders [article]

Svante Janson
2011 arXiv   pre-print
We study poset limits given by sequences of finite interval orders or, as a special case, finite semiorders.  ...  In the interval order case, we show that every such limit can be represented by a probability measure on the space of closed subintervals of [0,1], and we define a subset of such measures that yield a  ...  The purpose of the present paper is to study the special cases of limits of interval orders and semiorders. (Cf. the related study of interval graph limits in [7] .)  ... 
arXiv:1104.1264v1 fatcat:mpzaqgx4dbfgpd4q36ghlncbne

ENUMERATION OF MIXED LINEAR MODELS AND A SAS MACRO FOR COMPUTATION OF CONFIDENCE INTERVALS FOR VARIANCE COMPONENTS

Ann Hess, Hari Iyer
2001 Conference on Applied Statistics in Agriculture  
The enumeration of nonisomorphic posets is an interesting and nontrivial combinatorial problem for which answers are available for posets of order 14 or less, i.e. for fixed effects ANOVA models with 14  ...  It is well known that there is a one-to-one correspondence between fixed effects ANOVA models involving both crossed and nested factors, and combinatorial objects called "posets".  ...  Table 1 : 1 Number of Unlabelled Po sets with n Elements I n I Unlabelled Posets I Lygeros and P.  ... 
doi:10.4148/2475-7772.1215 fatcat:5p3yxz7hl5ebleesfprzbgmfqm

Limits of interval orders and semiorders

Svante Janson
2012 Journal of Combinatorics  
We study poset limits given by sequences of finite interval orders or, as a special case, finite semiorders.  ...  In the interval order case, we show that every such limit can be represented by a probability measure on the space of closed subintervals of [0, 1], and we define a subset of such measures that yield a  ...  The purpose of the present paper is to study the special cases of limits of interval orders and semiorders. (Cf. the related study of interval graph limits in [7] .)  ... 
doi:10.4310/joc.2012.v3.n2.a2 fatcat:pu6m6ckfjjfchc6oszfy6rnqwu

Page 654 of Mathematical Reviews Vol. , Issue 94b [page]

1994 Mathematical Reviews  
For a finite ranked poset P, denote by a(P) the maximum number of elements of P that can be taken with no two of them simulta- neously in some interval of P, and by p(P) the minimum number  ...  Two special classes of irre- ducible T-modules, called thin and dual-thin, are introduced.  ... 

The database of interval orders difficult for the jump number minimizing algorithms

Przemysław Krysztowiak
2011 Annales UMCS Informatica  
In this paper, we are investigating a restricted class of posets, called interval orders, admitting approximation algorithms for the jump number problem, in which the problem remains NP-complete.  ...  The problems of scheduling jobs on a single machine subject to precedence constraints can often be modelled as the jump number problem for posets, where a linear extension of a given partial order is to  ...  We have tried to generate the random intervals from both the uniform distribution and the exponential distributions.  ... 
doi:10.2478/v10065-011-0025-4 fatcat:t6e7o7ppincpvd6x5c24to77eq

Author index to volume 144 (1995)

1995 Discrete Mathematics  
West, Interval number of special posets and random posets  ...  Triesch and Z. Tuza, Searching for acyclic orientations of graphs (1-3) 3 10 Erd6s, P.L., U. Faigle and W. Kern, On the average rank of LYM-sets (1-3) 11-22 Faigle, U., see P.L. Erd6s , H.A. and J.  ... 
doi:10.1016/0012-365x(95)90075-v fatcat:svbdmbjjlzaqbfttxktpvdtesq

On intervals of the consecutive pattern poset

Sergi Elizalde, Peter R. W. McNamara
2020 Discrete Mathematics & Theoretical Computer Science  
We study the structure of the intervals in this poset from topological, poset-theoretic, and enumerative perspectives.  ...  In particular, we prove that all intervals are rank-unimodal and strongly Sperner, and we characterize disconnected and shellable intervals.  ...  For example, in Characterization of disconnected intervals It will be helpful to deal with posets of rank 2 separately because we can completely classify them, and because they sometimes require special  ... 
doi:10.46298/dmtcs.6380 fatcat:pdfm7al7fzasvmhpmdwwn55roy

Sorting and Selection in Posets [chapter]

Constantinos Daskalakis, Richard M. Karp, Elchanan Mossel, Samantha Riesenfeld, Elad Verbin
2009 Proceedings of the Twentieth Annual ACM-SIAM Symposium on Discrete Algorithms  
In particular, we present the first algorithm that sorts a width-w poset of size n with optimal query complexity O(n(w + log n)).  ...  Classical problems of sorting and searching assume an underlying linear ordering of the objects being compared.  ...  We present upper and lower bounds on the query and total complexity of k-selection, for deterministic and randomized computational models, for the special case of k = 1 as well as the general case.  ... 
doi:10.1137/1.9781611973068.44 fatcat:kil4vzenarcutflw4q5ueis4ga

Sorting and Selection in Posets

Constantinos Daskalakis, Richard M. Karp, Elchanan Mossel, Samantha J. Riesenfeld, Elad Verbin
2011 SIAM journal on computing (Print)  
In particular, we present the first algorithm that sorts a width-w poset of size n with optimal query complexity O(n(w + log n)).  ...  Classical problems of sorting and searching assume an underlying linear ordering of the objects being compared.  ...  We present upper and lower bounds on the query and total complexity of k-selection, for deterministic and randomized computational models, for the special case of k = 1 as well as the general case.  ... 
doi:10.1137/070697720 fatcat:ejhc3uvpdzayrcwe7w5k4hjise

Dynamic Threshold Strategy for Universal Best Choice Problem

Jakub Kozik
2010 Discrete Mathematics & Theoretical Computer Science  
We present its partial analysis which is sufficient to prove that the probability of success with this strategy is asymptotically strictly greater than 1/4, which is the value of the best universal strategy  ...  We put also ltr(m) = 1 − tr(m) and ltr n (m) = n − tr n (m). For a fixed poset P , we usually denote by m the number of its maximal elements, and by n the number of all its elements.  ...  the number of maximal elements of the induced poset at time t.  ... 
doi:10.46298/dmtcs.2767 fatcat:k3qbvlwcgbe6zn2xkfvyhas3ki

Fuzzification of probabilistic objects

Martin Papco
2013 Proceedings of the 8th conference of the European Society for Fuzzy Logic and Technology  
Using our previous results, we show that the category ID of D-posets of fuzzy sets provides a framework in which the transition from classical to fuzzy probability theory is the consequence of some natural  ...  We introduce two categories CP and FP of probability spaces and observables corresponding to the classical probability theory and the fuzzy probability theory, respectively.  ...  random variables enable to tell a story in the costumes of real numbers (measurements) and, finally, observables provide effective tools to compare two dramas.  ... 
doi:10.2991/eusflat.2013.10 dblp:conf/eusflat/Papco13 fatcat:6r5vdfhmijd77acrgq2nuy7lau

Linear Extensions and Comparable Pairs in Partial Orders

Colin McDiarmid, David Penman, Vasileios Iliopoulos
2017 Order  
We also consider a random interval partial order on n elements, which has close to a third of the pairs comparable with high probability: we show that the number of linear extensions is n!  ...  We study the number of linear extensions of a partial order with a given proportion of comparable pairs of elements, and estimate the maximum and minimum possible numbers.  ...  We are grateful to the referees, whose comments have led to a much improved paper, and have encouraged us for example to make explicit the Conjectures 12 and 13.  ... 
doi:10.1007/s11083-017-9439-y fatcat:kzaqgrajtzeqfltnxd4bbtz2l4

On the Approximability of Single-Machine Scheduling with Precedence Constraints

Christoph Ambühl, Monaldo Mastrolilli, Nikolaus Mutsanas, Ola Svensson
2011 Mathematics of Operations Research  
Our approach yields the best-known approximation ratios for all previously considered special classes of precedence constraints, and it provides the first results for bounded degree and orders of interval  ...  On the negative side, we show that the addressed problem remains NP-hard even when restricted to the special case of interval orders.  ...  Different parts of this work have appeared in preliminary form in APPROX'06, IPCO'07, and FOCS'07.  ... 
doi:10.1287/moor.1110.0512 fatcat:agx7hey6ojf3vkrghfuu6jalfq
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