scholarly journals Counting Linear Extensions of Restricted Posets

10.37236/8552 ◽  
2020 ◽  
Vol 27 (4) ◽  
Author(s):  
Sam Dittmer ◽  
Igor Pak
Keyword(s):  
Linear Extensions

We prove the 1991 conjecture by Brightwell and Winkler that counting the number of linear extensions for posets of height two is #P-complete. We further extend this result to incidence posets of graphs.

scholarly journals Accidental Gauge Symmetries of Minkowski Spacetime in Teleparallel Theories

Universe ◽  
2021 ◽  
Vol 7 (5) ◽  
pp. 143
Author(s):  
Jose Beltrán Jiménez ◽  
Tomi S. Koivisto
Keyword(s):  
General Relativity ◽  
Minkowski Spacetime ◽  
Linear Extensions ◽  
Gauge Symmetries ◽  
Linear Spectrum ◽  
Massless Spin ◽  
Non Linear ◽  
Common Framework ◽  
Local Symmetries ◽  
Quadratic Action

In this paper, we provide a general framework for the construction of the Einstein frame within non-linear extensions of the teleparallel equivalents of General Relativity. These include the metric teleparallel and the symmetric teleparallel, but also the general teleparallel theories. We write the actions in a form where we separate the Einstein–Hilbert term, the conformal mode due to the non-linear nature of the theories (which is analogous to the extra degree of freedom in f(R) theories), and the sector that manifestly shows the dynamics arising from the breaking of local symmetries. This frame is then used to study the theories around the Minkowski background, and we show how all the non-linear extensions share the same quadratic action around Minkowski. As a matter of fact, we find that the gauge symmetries that are lost by going to the non-linear generalisations of the teleparallel General Relativity equivalents arise as accidental symmetries in the linear theory around Minkowski. Remarkably, we also find that the conformal mode can be absorbed into a Weyl rescaling of the metric at this order and, consequently, it disappears from the linear spectrum so only the usual massless spin 2 perturbation propagates. These findings unify in a common framework the known fact that no additional modes propagate on Minkowski backgrounds, and we can trace it back to the existence of accidental gauge symmetries of such a background.

scholarly journals Linear Extensions of N-free Orders

Order ◽  
2014 ◽  
Vol 32 (2) ◽  
pp. 147-155 ◽  
Author(s):  
Stefan Felsner ◽  
Thibault Manneville
Keyword(s):  
Linear Extensions

Added Resistance in Seaways and its Impact on Yacht Performance

2007 ◽  
Author(s):  
Kai Graf ◽  
Marcus Pelz ◽  
Volker Bertram ◽  
H. Söding
Keyword(s):  
Strong Impact ◽  
Wave Spectra ◽  
Linear Extensions ◽  
Added Resistance ◽  
Optimum Length ◽  
Prediction Program ◽  
Strip Theory ◽  
Velocity Prediction ◽  
Added Resistance In Waves ◽  
Response Amplitude Operators

A method for the prediction of seakeeping behaviour of sailing yachts has been developed. It is based on linear strip theory with some non-linear extensions. The method is capable to take into account heeling and yawing yacht hulls, yacht appendages and sails. The yacht's response amplitude operators (RAO) and added resistance in waves can be predicted for harmonic waves as well as for natural wave spectra. The method is used to study added resistance in seaways for ACC-V5 yachts of varying beam. Results are used for further VPP investigations. The AVPP velocity prediction program is used to study optimum length to beam ratio of the yachts depending on wind velocity and upwind to downwind weighting. This investigation is carried out for flat water conditions as well as for two typical wave spectra. The results show that taking into account added resistance in seaways has a strong impact on predicted performance of the yacht.

scholarly journals Linear extensions of some Baire-one functions

2017 ◽  
Vol 110 (2) ◽  
pp. 175-182 ◽  
Author(s):  
Waldemar Sieg
Keyword(s):  
Linear Extensions ◽  
Baire One

scholarly journals Linear Extensions and Comparable Pairs in Partial Orders

Order ◽  
2017 ◽  
Vol 35 (3) ◽  
pp. 403-420 ◽  
Author(s):  
Colin McDiarmid ◽  
David Penman ◽  
Vasileios Iliopoulos
Keyword(s):  
Partial Orders ◽  
Linear Extensions
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