Related papers: Boolean complexes for Ferrers graphs
We show that $\Gamma$-free fillings and lonesum fillings of Ferrers shapes are equinumerous by applying a previously defined bijection on matrices for this more general case and by constructing a new bijection between Callan sequences and…
We compute the graded Betti numbers for the toric ideal of a family of graphs constructed by adjoining a cycle to a complete bipartite graph. The key observation is that this family admits an initial ideal which has linear quotients. As a…
We present the Boolean dimension of a graph, we relate it with the notions of inner, geometric and symplectic dimensions, and with the rank and minrank of a graph. We obtain an exact formula for the Boolean dimension of a tree in terms of a…
We establish explicit formulas for Bell numbers and graphical Stirling numbers of complete multipartite graphs, complete bipartite graphs with removed perfect matchings, and Mycielskian trees. For complete multipartite graphs…
This paper investigates the rational Betti numbers of real toric manifolds associated with chordal nestohedra. We consider the poset topology of a specific poset induced from a chordal building set, and show its EL-shellability. Based on…
In this paper we study some algebraic properties of hypergraphs, in particula their Betti numbers. We define some different types of complete hypergraphs, which to the best of our knowledge, are not previously considered in the literature.…
In this brief note, we give two explicit formulas for the Bernoulli Numbers in terms of the Stirling numbers of the second kind, and the Eulerian Numbers. To the best of our knowledge, these formulas are new. We also derive two more…
We consider the line graph of a pure simplicial complex. We prove that, as in the case of line graphs of simple graphs, one can compute the second graded Betti number of the facet ideal of a pure simplicial complex in terms of the…
A Ferrers rook graph is a graph whose vertices correspond to the dots in a Ferrers diagram, and where two vertices are adjacent if they are in the same row or the same column. We propose a conjectural formula for the gonality of Ferrers…
In this paper, we consider the degenerate poly-Bernoulli polynomials and present new and explicit formulas for computing them in terms of the degenerate Bernoulli polynomials and Stirling numbers of the second kind.
Let P be the set of the sequence of polynomials of degree n. The aim of this paper is to study the Stirling numbers of the second kind associated with P and of the first kind associated with P, in a unified and systematic way with the help…
In earlier work the Kauffman bracket polynomial was extended to an invariant of marked graphs, i.e., looped graphs whose vertices have been partitioned into two classes (marked and not marked). The marked-graph bracket polynomial is readily…
Ferrer dimension, along with the order dimension, is a standard dimensional concept for bipartite graphs. In this paper, we prove that a graph is of Ferrer dimension three (equivalent to the intersection bigraph of orthants and points in…
We discuss the problem of counting vertices in Gelfand-Zetlin polytopes. Namely, we deduce a partial differential equation with constant coefficients on the exponential generating function for these numbers. For some particular classes of…
In this paper, applying the Fa\`a di Bruno formula and some properties of Bell polynomials, several closed formulas and determinantal expressions involving Stirling numbers of the second kind for higher-order Bernoulli and Euler polynomials…
In this paper, using geometric polynomials, we obtain a generating function of p-Bernoulli numbers. As a consequences this generating function, we derive closed formulas for the finite summation of Bernoulli and harmonic numbers involving…
In the paper, the authors provide four alternative proofs of an explicit formula for computing Bernoulli numbers in terms of Stirling numbers of the second kind.
We study the enumeration of set partitions, according to their length, number of parts, cyclic type, and genus. We introduce genus-dependent Bell, Stirling numbers, and Fa\`a di Bruno coefficients. Besides attempting to summarize what is…
We introduce a novel approach named the {\it induced-subgraph approach} for investigating the Betti numbers of normal edge rings. Utilizing this approach, we compute all the multi-graded Betti numbers of the edge rings associated with…
Starting with an isolated vertex, here we construct a threshold hypergraph by repeatedly adding an isolated vertex or a $k$-dominating vertex set. We represent a threshold hypergraph by a string of non-negative integers and find the…