𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Geometrical Techniques for Estimating Numbers of Linear Extensions

✍ Scribed by Béla Bollobás; Graham Brightwell; Alexander Sidorenko

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
126 KB
Volume
20
Category
Article
ISSN
0195-6698

No coin nor oath required. For personal study only.

✦ Synopsis

Let P be a two-dimensional order, and P any complement of P, i.e., any partial order whose comparability graph is the complement of the comparability graph of P. Let e(Q) denote the number of linear extensions of the partial order Q. Sidorenko [13] showed that e(P)e(P) ≥ n!, for any two-dimensional partial order P. In this note, we use results from polyhedral combinatorics, and from the geometry of R n , to give a companion upper bound on e(P)e(P), as well as an alternative proof of the lower bound. We use these results to obtain bounds on the number of linear extensions of a random two-dimensional partial order.

📜 SIMILAR VOLUMES

Error estimation for geometrically non-l
Error estimation for geometrically non-linear analysis of framed structures
✍ B. A. Izzuddin; A. Chew; D. Lloyd Smith 📂 Article 📅 2004 🏛 John Wiley and Sons 🌐 English ⚖ 259 KB

## Abstract This paper is concerned with the estimation of errors that arise in the geometrically non‐linear analysis of framed structures using 1D beam‐column finite elements. A quartic element is used to illustrate specific issues of error estimation relating to geometrically non‐linear analysis,

EXTENSIONS OF THE PHASE SPACE LINEARIZAT
EXTENSIONS OF THE PHASE SPACE LINEARIZATION (PSL) TECHNIQUE FOR NON-LINEAR OSCILLATORS
✍ R.N. Iyengar; D. Roy 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 482 KB

This paper is devoted to further exploration of the PSL technique developed earlier in its companion paper. To start with, it is shown that the method is not only appicable for obtaining one-periodic orbits, but can be made use of for obtaining every conceivable orbit, including subharmonic or perio

Linearized and non-linear acoustic/visco
Linearized and non-linear acoustic/viscous splitting techniques for low Mach number flows
✍ Mohammad Farshchi; Siamak K. Hannani; Mohammad Ebrahimi 📂 Article 📅 2003 🏛 John Wiley and Sons 🌐 English ⚖ 171 KB

## Abstract Computation of the acoustic disturbances generated by unsteady low‐speed flow fields including vortices and shear layers is considered. The equations governing the generation and propagation of acoustic fluctuations are derived from a two‐step acoustic/viscous splitting technique. An op

ESTIMATION OF MODAL PARAMETERS THROUGH A
ESTIMATION OF MODAL PARAMETERS THROUGH A NON-LINEAR OPTIMISATION TECHNIQUE
✍ LUIZ FERNANDO LOMBA ROSA; CARLOS MAGLUTA; NEY ROITMAN 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 183 KB

The estimation of modal parameters through Goal Programming, an optimisation technique, is presented. The estimation, performed in the frequency domain, seeks to minimise the total squared error between experimental and estimated values of the frequency response functions. Its purpose is to obtain g