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## Filters

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Interval number of special posets and random posets

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. ...

##
###
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*).” ...

##
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Limits of interval orders and semiorders
[article]

2011
*
arXiv
*
pre-print

We study

arXiv:1104.1264v1
fatcat:mpzaqgx4dbfgpd4q36ghlncbne
*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] .) ...##
###
ENUMERATION OF MIXED LINEAR MODELS AND A SAS MACRO FOR COMPUTATION OF CONFIDENCE INTERVALS FOR VARIANCE COMPONENTS

2001
*
Conference on Applied Statistics in Agriculture
*

The enumeration

doi:10.4148/2475-7772.1215
fatcat:5p3yxz7hl5ebleesfprzbgmfqm
*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. ...##
###
Limits of interval orders and semiorders

2012
*
Journal of Combinatorics
*

We study

doi:10.4310/joc.2012.v3.n2.a2
fatcat:pu6m6ckfjjfchc6oszfy6rnqwu
*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] .) ...##
###
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

2011
*
Annales UMCS Informatica
*

In this paper, we are investigating a restricted class

doi:10.2478/v10065-011-0025-4
fatcat:t6e7o7ppincpvd6x5c24to77eq
*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. ...##
###
Author index to volume 144 (1995)

1995
*
Discrete Mathematics
*

West,

doi:10.1016/0012-365x(95)90075-v
fatcat:svbdmbjjlzaqbfttxktpvdtesq
*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. ...##
###
On intervals of the consecutive pattern poset

2020
*
Discrete Mathematics & Theoretical Computer Science
*

We study the structure

doi:10.46298/dmtcs.6380
fatcat:pdfm7al7fzasvmhpmdwwn55roy
*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*...##
###
Sorting and Selection in Posets
[chapter]

2009
*
Proceedings of the Twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
*

In particular, we present the first algorithm that sorts a width-w

doi:10.1137/1.9781611973068.44
fatcat:kil4vzenarcutflw4q5ueis4ga
*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. ...##
###
Sorting and Selection in Posets

2011
*
SIAM journal on computing (Print)
*

In particular, we present the first algorithm that sorts a width-w

doi:10.1137/070697720
fatcat:ejhc3uvpdzayrcwe7w5k4hjise
*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. ...##
###
Dynamic Threshold Strategy for Universal Best Choice Problem

2010
*
Discrete Mathematics & Theoretical Computer Science
*

We present its partial analysis which is sufficient to prove that the probability

doi:10.46298/dmtcs.2767
fatcat:k3qbvlwcgbe6zn2xkfvyhas3ki
*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. ...##
###
Fuzzification of probabilistic objects

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

doi:10.2991/eusflat.2013.10
dblp:conf/eusflat/Papco13
fatcat:6r5vdfhmijd77acrgq2nuy7lau
*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. ...##
###
Linear Extensions and Comparable Pairs in Partial Orders

2017
*
Order
*

We also consider a

doi:10.1007/s11083-017-9439-y
fatcat:kzaqgrajtzeqfltnxd4bbtz2l4
*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. ...##
###
On the Approximability of Single-Machine Scheduling with Precedence Constraints

2011
*
Mathematics of Operations Research
*

Our approach yields the best-known approximation ratios for all previously considered

doi:10.1287/moor.1110.0512
fatcat:agx7hey6ojf3vkrghfuu6jalfq
*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. ...
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