Given a finite relational language L, a hereditary L-property is a class of finite Lstructures which is closed under isomorphism and model theoretic substructure. This notion encompasses many objects of study in extremal combinatorics, including (but not limited to) hereditary properties of graphs, hypergraphs, and oriented graphs. In this paper, we generalize certain definitions, tools, and re...

Our first result provides a new characterization of Auslander algebras using property hereditary torsion pairs. The second shows an algebra $\Lambda$ is left or right glued if and only representation-finite. Finally, our third the module category any contains tilting with particular property, which we call property. Applications this are investigated.

In this paper, we discuss the relation between shellability, sequentially CohenMacaulayness, and partitionability. Especially, our main concern is to see the difference of these properties when we require heredity. For a property P, we say a simplicial complex satisfies hereditary-P if the simplicial complex itself and all the restrictions to subsets of its vertex set satisfy the property P, an...

We study the relation between the growth rate of a graph property and the entropy of the graph limits that arise from graphs with that property. In particular, for hereditary classes we obtain a new description of the colouring number, which by well-known results describes the rate of growth. We study also random graphs and their entropies. We show, for example, that if a hereditary property ha...

An additive hereditary graph property is a set of graphs, closed under isomorphism and under taking subgraphs and disjoint unions. Let P1, . . . ,Pn be additive hereditary graph properties. A graph G has property (P1 ◦ · · · ◦Pn) if there is a partition (V1, . . . , Vn) of V (G) into n sets such that, for all i, the induced subgraph G[Vi] is in Pi. A property P is reducible if there are propert...

An additive induced-hereditary property of graphs is any class of finite simple graphs which is closed under isomorphisms, disjoint unions and induced subgraphs. The set of all additive induced-hereditary properties of graphs, partially ordered by set inclusion, forms a completely distributive lattice. We introduce the notion of the join-decomposability number of a property and then we prove th...

Given an in…nite hereditary property of graphs P; the principal extremal parameter of P is the value (P) = lim n!1 n 2 1 maxfe (G) : G 2 P and v (G) = ng: The Erd1⁄2os-Stone theorem gives (P) if P is monotone, but this result does not apply to hereditary P. Thus, one of the results of this note is to establish (P) for any hereditary property P: Similar questions are studied for the parameter (p...

‎Let $S$ be an inverse semigroup with the set of idempotents $E$‎. We prove that the semigroup algebra $ell^{1}(S)$ is always‎ ‎$2n$-weakly module amenable as an $ell^{1}(E)$-module‎, ‎for any‎ ‎$nin mathbb{N}$‎, ‎where $E$ acts on $S$ trivially from the left‎ ‎and by multiplication from the right‎. ‎Our proof is based on a common fixed point property for semigroups‎.  

We investigate a new property of computing systems called weak stabilization. Although this property is strictly weaker than the well-known property of stabilization, weak stabilization is superior to stabilization in several respects. In particular, adding delays to a system preserves the system property of weak stabilization, but does not necessarily preserve its stabilization property. Becau...