Related papers: Characterization of Cobweb Posets as KoDAGs
The characterization of fibonacci cobweb poset as d.a.g. and o.d.a.g. is given. The dim 2 poset such that its hasse diagram coincide with digraf of fibonacci cobweb poset is constructed.
A digraph that represents reasonably a scheduling problem should be a directed acyclic graph. Here down we shall deal with special kind of graded $DAGs$ named $KoDAGs$. For their definition and first primary properties see $ [1]$, where…
Natural join of $di-bigraphs$ that is directed biparted graphs and their corresponding adjacency matrices is defined and then applied to investigate the so called cobweb posets and their $Hasse$ digraphs called $KoDAGs$. $KoDAGs$ are…
The explicite formulas for Mobius function and some other important elements of the incidence algebra of an arbitrary cobweb poset are delivered. For that to do one uses Kwasniewski's construction of his cobweb posets . The digraph…
One considers here orderable acyclic digraphs named KoDAGs which represent the outmost general chains of dibicliques denoting thus the outmost general chains of binary relations. Because of this fact KoDAGs start to become an outstanding…
After identifying the reduced incidence algebra of an arbitrary cobweb poset the very first properties of these algebras are being disclosed.
Cobweb posets uniquely represented by directed acyclic graphs are such a generalization of the Fibonacci tree that allows joint combinatorial interpretation for all of them under admissibility condition. This interpretation was derived in…
One introduces here the natural join $P \os Q$ of graded posets $< P,\leq_P >$ and $< Q,\leq_Q >$ with correspondingly maximal and minimal sets being identical as expressed by ordinal sum $P\oplus Q$ apart from other definition and due to…
A class of new type graded infinite posets with minimal element are considered. These so called cobweb posets introduced recently by the present author provide a wide range of new noncommutative prefab combinatorial schema with…
We characterize Cohen-Macaulay posets of dimension two; they are precisely the shellable and strongly connected posets of dimension two. We also give a combinatorial description of these posets. Using the fact that co-comparability graph of…
A chain poset, by definition, consists of chains of ordered elements in a poset. We study the chain posets associated to two posets: the Boolean algebra and the poset of isotropic flags. We prove that, in both cases, the chain posets…
We introduce a new family of finite posets which we call 2-chains. These first arose in the study of 0-Hecke algebras, but they admit a variety of different characterisations. We give these characterisations, prove that they are equivalent…
This note is a response to one of problems posed by A.K. Kwasniewski in one of his recent papers. Namely for the sequence of finite cobweb subposets, the looked for explicit formulas for corresponding sequence of characteristic polynomials…
Kwasniewski's cobweb posets uniquely represented by directed acyclic graphs are such a generalization of the Fibonacci tree that allows joint combinatorial interpretation for all of them under admissibility condition. This interpretation…
In 2010, M. Studen\'y, R. Hemmecke, and S. Linder explored a new algebraic description of graphical models, called characteristic imsets. Compare with standard imsets, characteristic imsets have several advantages: they are still unique…
F-boxes defined in [6] as hyper-boxes in N^{\infty} discrete space were applied here for the geometric description of the cobweb posetes Hasse diagrams tilings. The F-boxes edges sizes are taken to be values of terms of natural numbers'…
The homset invariant of a knot or link L with respect to an algebraic knot coloring structure X can be identified with a set of colorings of a diagram of L by elements of X via an identification of diagrammatic generators with algebraic…
In addition to the three standard operations on posets which are dual of poset or ordinal and cardinal sums of partial ordered sets one adds the natural join of posets. This is especially natural natural join operation for graded posets…
We introduce and study additive posets. We show that the top homology group (with coefficients in Z/2Z) of a finite dimensional CW-complex carries a structure of an additive poset invariant under subdivisions. Applications to CW-complexes…
The way to arrive at formula of zeta matrix for any graded posets with the finite set of minimal elements is delivered following the first reference. This is being achieved via adjacency and zeta matrix description of bipartite digraphs…