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Interval number of special posets and random posets
1995
Discrete Mathematics
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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
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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]
2011
arXiv
pre-print
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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
2001
Conference on Applied Statistics in Agriculture
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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
2012
Journal of Combinatorics
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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
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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
2011
Annales UMCS Informatica
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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
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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
2020
Discrete Mathematics & Theoretical Computer Science
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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]
2009
Proceedings of the Twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
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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
2011
SIAM journal on computing (Print)
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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
2010
Discrete Mathematics & Theoretical Computer Science
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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
2013
Proceedings of the 8th conference of the European Society for Fuzzy Logic and Technology
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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
2017
Order
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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
2011
Mathematics of Operations Research
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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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