14 citations · 51 across the 15 of their papers we have counts for
6 papers · 1 filter
A simple combinatorial interpretation of certain generalized Bell and Stirling numbers
Pietro Codara, Ottavio M. D'Antona, Pavol Hell
In a series of papers, P. Blasiak et al. developed a wide-ranging generalization of Bell numbers (and of Stirling numbers of the second kind) that appears to be relevant to the so-…
Partitions of a Finite Partially Ordered Set
Pietro Codara
In this paper, we investigate the notion of partition of a finite partially ordered set (poset, for short). We will define three different notions of partition of a poset, namely,…
A Mathematica package to cope with partially ordered sets
Pietro Codara
Mathematica offers, by way of the package Combinatorics, many useful functions to work on graphs and ordered structures, but none of these functions was specific enough to meet the…
Making simple proofs simpler
Pietro Codara, Ottavio M. D'Antona, Francesco Marigo +1
An open partition π [Cod09a, Cod09b] of a tree T is a partition of the vertices of T with the property that, for each block B of π, the upset of B is a union of blocks of π. This p…
Building Bricks with Bricks, with Mathematica
Pietro Codara, Ottavio M. D'Antona, Daniele Filaretti
In this work we solve a special case of the problem of building an n-dimensional parallelepiped using a given set of n-dimensional parallelepipeds. Consider the identity x^3 = x(x-…
Investigating independent subsets of graphs, with Mathematica
Pietro Codara, Ottavio M. D'Antona
With this work we aim to show how Mathematica can be a useful tool to investigate properties of combinatorial structures. Specifically, we will face enumeration problems on indepen…