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Can transitive orientation make sandwich problems easier?

Michel Habib, David Kelly, Emmanuelle Lebhar, Christophe Paul
2007 Discrete Mathematics  
Two different types of problems should be considered depending on the transitivity of the orientation: the poset sandwich problems and the directed sandwich problems.  ...  ., their complements) admit one or more transitive orientations (each orientation is a partially ordered set or poset).  ...  A property − → defined on posets is a comparability invariant iff when a poset P satisfies − → then any transitive orientation of the comparability graph G of P also satisfies − → .  ... 
doi:10.1016/j.disc.2005.12.048 fatcat:o6sbwl26h5drjh2ho3tt36zlxu

Uniform random posets [article]

Patryk Kozieł, Małgorzata Sulkowska
2018 arXiv   pre-print
By "almost uniform" we understand that the distribution of generated posets converges in total variation to the uniform distribution.  ...  We propose a simple algorithm generating labelled posets of given size according to the almost uniform distribution.  ...  Time complexity of P G n,m The overall time complexity of our algorithm depends on the complexity of two procedures.  ... 
arXiv:1810.05446v1 fatcat:2qdnqmvfe5f7lcrxucryu75deu

Thin Posets, CW Posets, and Categorification [article]

Alex Chandler
2019 arXiv   pre-print
We find that CW posets, that is, face posets of regular CW complexes, satisfy conditions making them particularly suitable for the construction of such cohomology theories.  ...  Such a construction provides a framework for the categorification of a variety of familiar topological/combinatorial invariants: anything expressible as a rank-alternating sum over a thin poset.  ...  The author's work was supported partially by the project P31705 of the Austrian Science Fund.  ... 
arXiv:1911.05600v2 fatcat:peqyyvjphvejboiobwuehiafni

Barycentric subdivisions

Margaret Bayer
1988 Pacific Journal of Mathematics  
It is shown that barycentric subdivisions of connected polyhedral complexes with at least two facets determine the underlying complex uniquely up to duality.  ...  Connections with the algorithmic theory of comparability graphs are discussed. The /-vectors of regular CW spheres are characterized.  ...  Please propose a heading for the odd numbered pages of less than 35 characters. Manuscripts, in triplicate, may be sent to any one of the editors. Please classify according to the scheme of Math.  ... 
doi:10.2140/pjm.1988.135.1 fatcat:53b7fgcsffeptp26ncda6p5hyi

Causal set dynamics: a toy model

A Criscuolo, H Waelbroeck
1999 Classical and quantum gravity  
Most notably, instead of the single phase transition of classical percolation, the quantum model displays two distinct crossover points.  ...  We construct a quantum measure on the power set of non-cyclic oriented graphs of N points, drawing inspiration from 1-dimensional directed percolation.  ...  The authors wish to express their gratitude to Rafael Sorkin who has been one of the chief motivators of this project.  ... 
doi:10.1088/0264-9381/16/6/315 fatcat:rsxmqiuruzdhnbwl47bzvddrya

Page 6938 of Mathematical Reviews Vol. , Issue 95k [page]

1995 Mathematical Reviews  
Gréger, Hans Dietmar Does transitivity help?  ...  The decision tree complexity of properties of partially ordered sets (posets) is considered.  ... 

Coproduct Transformations on Lattices of Closed Partial Orders [chapter]

Gemma Casas-Garriga, José L. Balcázar
2004 Lecture Notes in Computer Science  
complexity of the mining operation for the partial orders directly from the data.  ...  on a simpler graph of so-called stable sequences.  ...  Acknowledgements: The authors specially thank Elvira Pino for her useful explanations on category theory.  ... 
doi:10.1007/978-3-540-30203-2_24 fatcat:v3k3jzbmhjaetiu6maqcrwp4ia

Analyzing Variability in Product Families through Canonical Feature Diagrams

Jessie Carbonnel, Marianne Huchard, Clémentine Nebut
2017 Proceedings of the 29th International Conference on Software Engineering and Knowledge Engineering  
We outline its construction and we give insights about its shape and use when it is used as an alternative representation of wikipedia PCMs in the domain of software.  ...  In this paper, we investigate the benefits of a new structure, which captures variability in a canonical graphical representation.  ...  Reference [9] details the complexity of construction of the AC-poset (concept enumeration and transitive reduction computation) which is in Op|A| 2ˆ| O| 2`| A| 3 q.  ... 
doi:10.18293/seke2017-087 dblp:conf/seke/CarbonnelHN17 fatcat:fytujnbbgfbmpnjyai6qexpm2e

Spectral Gap for Random-to-Random Shuffling on Linear Extensions

Arvind Ayyer, Anne Schilling, Nicolas M. Thiéry
2016 Experimental Mathematics  
We conjecture that the second largest eigenvalue of the transition matrix is bounded above by (1+1/n)(1-2/n) with equality when the poset is disconnected.  ...  In this paper, we propose a new Markov chain which generalizes random-to-random shuffling on permutations to random-to-random shuffling on linear extensions of a finite poset of size n.  ...  Although the order-reversal property does not hold in general, one could hope that it holds under certain additional conditions.  ... 
doi:10.1080/10586458.2015.1107868 fatcat:imprvcasnnbshghdg3nkngp6ie

On Order Ideals of Minuscule Posets III: The CDE Property [article]

David B Rush
2016 arXiv   pre-print
Recent work of Hopkins establishes that the lattice of order ideals of a minuscule poset satisfies the coincidental down-degree expectations property of Reiner, Tenner, and Yong.  ...  The blueprint follows that of Rush and Wang in their uniform proof that various cardinality statistics are homomesic on orbits of order ideals of minuscule posets under the Fon-Der-Flaass action.  ...  Then V λ is minuscule with minuscule weight λ if the action of W on Λ λ is transitive. The last ingredient in the definition of a minuscule poset is a partial order on the weights Λ λ .  ... 
arXiv:1607.08018v1 fatcat:jdtnwpwr6nc5hfk22vuvdwf2ky

Estimating Octanol / Water Partition Coefficients by Order Preserving Mappings

Rainer Bruggemann, Guillermo Restrepo
2013 Croatica Chemica Acta  
Despite the satisfactory results found by Klein's methods, we think it is worth exploring another feature of the poset of chemicals used in Klein's approaches, namely the average posetic height, h av ,  ...  The basic idea is to deduce from order relations among chemicals, properties of the ordered chemicals.  ...  The similarity between Taylor series and this expansion has been studied by Nava et al. 38 This method does not require knowing the property values for the nearest neighbours of the substance one is  ... 
doi:10.5562/cca2296 fatcat:ybmscfr63becnm4ukdhc3t76m4

An algebra of concurrent non-deterministic processes

Ludmila A. Cherkasova, Vadim E. Kotov
1991 Theoretical Computer Science  
This paper illustrates how early ideas and simple naive concepts of concurrency theory of the 1960s have now turned into complex and subtle problems of modern calculi of concurrent processes.  ...  An algebra of finite processes AFP, is discussed as an example of research which incorporates various aspects of typical process calculi: axiomatization of the proposed algebra, adequate description of  ...  This is a definition of partial process properties on the semantical level.  ... 
doi:10.1016/0304-3975(91)90304-k fatcat:uvwsrd7t3nbuzogpidywpra5ri

On non-conjugate Coxeter elements in well-generated reflection groups

Victor Reiner, Vivien Ripoll, Christian Stump
2015 Discrete Mathematics & Theoretical Computer Science  
We also prove that there is a simply transitive action of the Galois group of the field of definition of $W$ on the set of conjugacy classes of Coxeter elements.  ...  International audience Given an irreducible well-generated complex reflection group $W$ with Coxeter number $h$, we call a Coxeter element any regular element (in the sense of Springer) of order $h$ in  ...  Acknowledgements The authors thank Jean Michel for many helpful discussions during the preparation of this work, as well as Alex Miller, both for helpful conversations and for pointing them to the results  ... 
doi:10.46298/dmtcs.2466 fatcat:vasz7g7suzbajo7jtk5yp74bx4

On non-conjugate Coxeter elements in well-generated reflection groups

Victor Reiner, Vivien Ripoll, Christian Stump
2016 Mathematische Zeitschrift  
We also prove that there is a simply transitive action of the Galois group of the field of definition of W on the set of conjugacy classes of Coxeter elements.  ...  Finally, we extend several of these properties to regular elements of arbitrary order.  ...  Acknowledgements The authors thank Jean Michel for many helpful discussions during the preparation of this work, as well as Alex Miller, both for helpful conversations and for pointing them to the results  ... 
doi:10.1007/s00209-016-1736-4 fatcat:gwixq2pme5dmbfyvltz7tjsaey

Homomorphism complexes, reconfiguration, and homotopy for directed graphs [article]

Anton Dochtermann, Anurag Singh
2021 arXiv   pre-print
Our construction can be seen as a special case of the poset structure on the set of multihomomorphisms in more general categories, as introduced by Kozlov, Matsushita, and others.  ...  We relate the topological properties of Hom complexes to certain digraph operations including products, adjunctions, and foldings.  ...  In this context one is interested in the connectivity and diameter of the complex − −− → Hom(𝐺, 𝑇 𝑛 ). We mostly study the case that 𝑇 𝑛 = − → 𝐾 𝑛 is an acyclic (or transitive) tournament.  ... 
arXiv:2108.10948v1 fatcat:egospqwryrdrlhybeecl2xtj3m
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