Related papers: Graded posets zeta matrix formula
We derive the explicit formula for the inverse of zeta matrix for any graded posets with the finite set of minimal elements . The combinatorial interpretation of this result is given. For that to do special number theoretic code triangles…
We present a matrix-theoretic approach for studying and enumerating finite posets through their incidence representations, referred to as poset matrices. Naturally labelled posets are encoded as Boolean lower triangular matrices, allowing a…
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…
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…
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…
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…
The set of all perfect matchings of a plane (weakly) elementary bipartite graph equipped with a partial order is a poset, moreover the poset is a finite distributive lattice and its Hasse diagram is isomorphic to $Z$-transformation directed…
In certain finite posets, the expected down-degree of their elements is the same whether computed with respect to either the uniform distribution or the distribution weighting an element by the number of maximal chains passing through it.…
Bipartitional relations were introduced by Foata and Zeilberger in their characterization of relations which give rise to equidistribution of the associated inversion statistic and major index. We consider the natural partial order on…
The Betti tables of a multigraded module encode the grades at which there is an algebraic change in the module. Multigraded modules show up in many areas of pure and applied mathematics, and in particular in topological data analysis, where…
A finite poset X carries a natural structure of a topological space. Fix a field k, and denote by D(X) the bounded derived category of sheaves of finite dimensional k-vector spaces over X. Two posets X and Y are said to be derived…
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 notion of level posets is introduced. This class of infinite posets has the property that between every two adjacent ranks the same bipartite graph occurs. When the adjacency matrix is indecomposable, we determine the length of the…
The coefficients of the chain polynomial of a finite poset enumerate chains in the poset by their number of elements. It has been a challenging open problem to determine which posets have real-rooted chain polynomials. Two new classes of…
We consider the matrix ${\frak Z}_P=Z_P+Z_P^t$, where the entries of $Z_P$ are the values of the zeta function of the finite poset $P$. We give a combinatorial interpretation of the determinant of ${\frak Z}_P$ and establish a recursive…
One-parameter criterion for 2-equipped posets with respect to cerepresentations is stated and proved. The list of sincere one-parameter 2-equipped posets is given as well as a complex matrix classification of all their indecomposables…
We present a method to compute integral cohomology of posets. This toolbox is applicable as soon as the sub-posets under each object possess certain structure. This is the case for simplicial complexes and simplex-like posets. The method is…
We propose a matrix approach for generating naturally labeled posets by representing each poset $P$ on the set $[n]$ as a Boolean poset matrix $A$. This algebraic representation enables a systematic handling of partial orderings through…
We introduce partially ordered sets (posets) with an additional structure given by a collection of vector subspaces of an algebra $A$. We call them algebraically equipped posets. Some particular cases of these, are generalized equipped…
We use model theoretic techniques to construct explicit first-order axiomatizations for the classes of posets that can be represented as systems of sets, where the order relation is given by inclusion, and existing meets and joins of…