57 citations · 120 across the 34 of their papers we have counts for
15 papers · 1 filter
On saturated triangulation-free convex geometric graphs
David Garber, Chaya Keller, Olga Nissenbaum +1
A convex geometric graph is a graph whose vertices are the corners of a convex polygon P in the plane and whose edges are boundary edges and diagonals of the polygon. It is called…
Analytic aspects of -analogue of poly-Stirling numbers of both kinds
Takao Komatsu, Eli Bagno, David Garber
The Stirling numbers of type of the second kind count signed set partitions. In this paper we provide new combinatorial and analytical identities regarding these numbers as wel…
The Worpitzky identity for the groups of signed and even-signed permutations
Eli Bagno, David Garber, Mordechai Novick
The well-known Worpitzky identity provides a connection between two bases of : The standard basis and the binomial basis , where the…
Signed partitions - A balls into urns approach
Eli Bagno, David Garber
Using Reiner's definition of Stirling numbers of type B of the second kind, we provide a 'balls into urns' approach for proving a generalization of a well-known identity concerning…
Some identities involving second kind Stirling numbers of types and
Eli Bagno, Riccardo Biagioli, David Garber
Using Reiner's definition of Stirling numbers of the second kind in types and , we generalize two well-known identities concerning the classical Stirling numbers of the seco…
Property testing and expansion in cubical complexes
David Garber, Uzi Vishne
We consider expansion and property testing in the language of incidence geometry, covering both simplicial and cubical complexes in any dimension. We develop a general method for p…
On Left regular bands and real Conic-Line arrangements
Michael Friedman, David Garber
An arrangement of curves in the real plane divides it into a collection of faces. In the case of line arrangements, there exists an associative product which gives this collection…
On the Orchard crossing number of prisms, ladders and other related graphs
Elie Feder, David Garber
This paper deals with the Orchard crossing number of some families of graphs which are based on cycles. These include disjoint cycles, cycles which share a vertex and cycles which…
On the Orchard crossing number of complete bipartite graphs
Elie Feder, David Garber
We compute the Orchard crossing number, which is defined in a similar way to the rectilinear crossing number, for the complete bipartite graphs K_{n,n}.
Eulerian partitions for configurations of skew lines
Roland Bacher, David Garber
In this paper, which is a complement of \cite{BG}, we study a few elementary invariants for configurations of skew lines, as introduced and analyzed first by Viro and his collabora…
On the excedance sets of colored permutations
Eli Bagno, David Garber, Robert Shwartz
We define the excedence set and the excedance word on , generalizing a work of Ehrenborg and Steingrimsson and use the inclusion-exclusion principle to calculate the numbe…
Towards the computation of the convex hull of a configuration from its corresponding separating matrix
Elie Feder, David Garber
In this paper, we cope with the following problem: compute the size of the convex hull of a configuration C, where the given data is the number of separating lines between any two…
Recursions for Excedance number in some permutations groups
Eli Bagno, David Garber, Toufik Mansour +1
The excedance number for S_n is known to have an Eulerian distribution. Nevertheless, the classical proof uses descents rather than excedances. We present a direct recursive proof…
Statistics on the multi-colored permutation groups
Eli Bagno, Ayelet Butman, David Garber
We define an excedance number for the multi-colored permutation group, i.e. the wreath product of Z_{r_1} x ... x Z_{r_k} with S_n, and calculate its multi-distribution with some n…
The Orchard crossing number of an abstract graph
Elie Feder, David Garber
We introduce the Orchard crossing number, which is defined in a similar way to the well-known rectilinear crossing number. We compute the Orchard crossing number for some simple fa…