𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Bipartite Posets of Finite Prinjective Type

✍ Scribed by Hans-Joachim von Höhne; Daniel Simson

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
351 KB
Volume
201
Category
Article
ISSN
0021-8693

No coin nor oath required. For personal study only.

✦ Synopsis

One of the main results of this paper is Theorem 1.2, which contains a characterization of finite bipartite posets I s IЈ j IЉ for which the category Ž . prin kI of prinjective modules over the incidence k-algebra kI of I is of finite representation type, where k is a field. In particular, it is shown that for any such Ž . poset I, the Auslander᎐Reiten quiver of the category prin kI has no oriented cycle, and there is a bijection between the isomorphism classes of indecomposable Ž .

I objects in prin kI and the positive roots of the quadratic form q associated with Ž . I. An existence of a preprojective component in prin kI is proved for faithful posets I which are ‫-ށ‬free.

📜 SIMILAR VOLUMES

Algebraic properties and dismantlability
Algebraic properties and dismantlability of finite posets
✍ Benoit Larose; László Zádori 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 554 KB

We show that every finite connected poser which admits certain operations such as Gumm or J6nsson operations, or a near unanimity function is dismantlable. This result is used to prove that a finite poset admits Gumm operations if and only if it admits a near unanimity function. Finite connected pos

Partitions of a finite three-complete po
Partitions of a finite three-complete poset
✍ Shiojenn Tseng; Muh-Chyi Horng 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 549 KB

Let P be a finite poset covered by three nonempty disjoint chains 7"1, T2, and T3. Suppose that p and q are different members of P. Also, P has the property that if p and q are in different chains and p < q, then P ---above{p} u below{q}. D.E. Daykin and J.W. Daykin (1985) made the conjecture: "Ther

Constructions of bipartite graphs from f
Constructions of bipartite graphs from finite geometries
✍ Keith E. Mellinger; Dhruv Mubayi 📂 Article 📅 2005 🏛 John Wiley and Sons 🌐 English ⚖ 99 KB 👁 1 views

## Abstract We construct an incidence structure using certain points and lines in finite projective spaces. The structural properties of the associated bipartite incidence graphs are analyzed. These __n__ × __n__ bipartite graphs provide constructions of __C__~6~‐free graphs with Ω(__n__^4/3^ edges