𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Generalized Δ–Y Exchange and k-Regular Matroids

✍ Scribed by James Oxley; Charles Semple; Dirk Vertigan

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
490 KB
Volume
79
Category
Article
ISSN
0095-8956

No coin nor oath required. For personal study only.

✦ Synopsis

This paper introduces a generalization of the matroid operation of 2 Y exchange. This new operation, segment cosegment exchange, replaces a coindependent set of k collinear points in a matroid by an independent set of k points that are collinear in the dual of the resulting matroid. The main theorem of the first half of the paper is that, for every field, or indeed partial field, F, the class of matroids representable over F is closed under segment cosegment exchanges. It follows that, for all prime powers q, the set of excluded minors for GF(q)-representability has at least 2 q&4 members. In the second half of the paper, the operation of segment cosegment exchange is shown to play a fundamental role in an excluded-minor result for k-regular matroids, where such matroids generalize regular matroids and Whittle's near-regular matroids.

📜 SIMILAR VOLUMES

Regular graphs constructed from the clas
Regular graphs constructed from the classical generalized quadrangle Q(4, q)
✍ L. Beukemann; K. Metsch 📂 Article 📅 2010 🏛 John Wiley and Sons 🌐 English ⚖ 144 KB 👁 1 views

Let c k be the smallest number of vertices in a regular graph with valency k and girth 8. It is known that c k+1 ≥ 2(1+k+k 2 +k 3 ) with equality if and only if there exists a finite generalized quadrangle of order k. No such quadrangle is known when k is not a prime power. In this case, small regul

Regular circular and compact semicircula
Regular circular and compact semicircular patch antennas with a T-probe feeding
✍ Y. X. Guo; K. M. Luk; K. F. Lee 📂 Article 📅 2001 🏛 John Wiley and Sons 🌐 English ⚖ 184 KB 👁 1 views

## Abstract Wideband T‐probe proximity‐fed regular circular and compact semicircular patch antennas are proposed in this paper. For the regular circular patch antenna, using a foam layer of thickness ∼0.13λ~0~ as a supported substrate, an impedance bandwidth of 35% and a gain of over 8.0 dBi have b

The conditional heteroscedasticity of th
The conditional heteroscedasticity of the yen–dollar exchange rate
✍ Y. K. Tse 📂 Article 📅 1998 🏛 John Wiley and Sons 🌐 English ⚖ 108 KB 👁 1 views

This paper examines the conditional heteroscedasticity of the yen±dollar exchange rate. A model is constructed by extending the asymmetric power autoregressive conditional heteroscedasticity model to a process that is fractionally integrated. It is found that, unlike the equity markets, the apprecia