Bound quivers of three-separate stratified posets, their Galois coverings and socle projective representations

Stanisław Kasjan

Displaying similar documents to “Bound quivers of three-separate stratified posets, their Galois coverings and socle projective representations”

On the distributions of $R_{m n}^{+} (j)$ and $(D_{m n}^{+}, R_{m n}^{+} (j))$

Jagdish Saran, Kanwar Sen (1982)

Aplikace matematiky

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The contents of the paper is concerned with the two-sample problem where $F_{m} (x)$ and $G_{n} (x)$ are two empirical distribution functions. The difference $F_{m} (x) - G_{n} (x)$ changes only at an $x_{i}, i = 1, 2, ..., m + n$ , corresponding to one of the observations. Let $R_{m n}^{+} (j)$ denote the subscript $i$ for which $F_{m} (x_{i}) - G_{n} (x_{i})$ achieves its maximum value $D_{m n}^{+}$ for the $j$ th time $(j = 1, 2, ...)$ . The paper deals with the probabilities for $R_{m n}^{+} (j)$ and for the vector $(D_{m n}^{+}, R_{m n}^{+} (j))$ under $H_{0} : F = G$ , thus generalizing the results of Steck-Simmons (1973). These results have been derived by applying the random walk model. ...

Representation-finite selfinjective algebras of class $D_{n}$

Christine Riedtmann (1983)

Compositio Mathematica

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Coalgebras, comodules, pseudocompact algebras and tame comodule type

Daniel Simson (2001)

Colloquium Mathematicae

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We develop a technique for the study of K-coalgebras and their representation types by applying a quiver technique and topologically pseudocompact modules over pseudocompact K-algebras in the sense of Gabriel [17], [19]. A definition of tame comodule type and wild comodule type for K-coalgebras over an algebraically closed field K is introduced. Tame and wild coalgebras are studied by means of their finite-dimensional subcoalgebras. A weak version of the tame-wild dichotomy theorem of...

A splitting theorem for multipeak path algebras

Daniel Simson (1991)

Fundamenta Mathematicae

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Simply connected right multipeak algebras and the separation property

Stanisław Kasjan (1999)

Colloquium Mathematicae

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Let R=k(Q,I) be a finite-dimensional algebra over a field k determined by a bound quiver (Q,I). We show that if R is a simply connected right multipeak algebra which is chord-free and $\tilde{}$ -free in the sense defined below then R has the separation property and there exists a preprojective component of the Auslander-Reiten quiver of the category prin(R) of prinjective R-modules. As a consequence we get in 4.6 a criterion for finite representation type of prin(R) in terms of the prinjective...

The standard form of a representation-finite algebra

O. Bretscher, P. Gabriel (1983)

Bulletin de la Société Mathématique de France

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Sets Expressible as Unions of Staircase $n$ -Convex Polygons

Marilyn Breen (2011)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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Let $k$ and $n$ be fixed, $k \geq 1$ , $n \geq 1$ , and let $S$ be a simply connected orthogonal polygon in the plane. For $T \subseteq S, T$ lies in a staircase $n$ -convex orthogonal polygon $P$ in $S$ if and only if every two points of $T$ see each other via staircase $n$ -paths in $S$ . This leads to a characterization for those sets $S$ expressible as a union of $k$ staircase $n$ -convex polygons $P_{i}$ , $1 \leq i \leq k$ .

Cycle and path embedding on 5-ary N-cubes

Tsong-Jie Lin, Sun-Yuan Hsieh, Hui-Ling Huang (2009)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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We study two topological properties of the 5-ary $n$ -cube $Q_{n}^{5}$ . Given two arbitrary distinct nodes $x$ and $y$ in $Q_{n}^{5}$ , we prove that there exists an $x$ - $y$ path of every length ranging from $2 n$ to $5^{n} - 1$ , where $n \geq 2$ . Based on this result, we prove that $Q_{n}^{5}$ is 5-edge-pancyclic by showing that every edge in $Q_{n}^{5}$ lies on a cycle of every length ranging from $5$ to $5^{n}$ .