14 citations · 51 across the 15 of their papers we have counts for
15 papers
Querying with Łukasiewicz logic
Stefano Aguzzoli, Pietro Codara, Tommaso Flaminio +2
In this paper we present, by way of case studies, a proof of concept, based on a prototype working on a automotive data set, aimed at showing the potential usefulness of using form…
Valuations in Nilpotent Minimum Logic
Pietro Codara, Diego Valota
The Euler characteristic can be defined as a special kind of valuation on finite distributive lattices. This work begins with some brief consideration on the role of the Euler char…
Generalized Fibonacci and Lucas cubes arising from powers of paths and cycles
Pietro Codara, Ottavio M. D'Antona
The paper deals with some generalizations of Fibonacci and Lucas sequences, arising from powers of paths and cycles, respectively. In the first part of the work we provide a formul…
Eulerian digraphs and Dyck words, a bijection
Pietro Codara, Ottavio M. D'Antona, Marco Genuzio
The main goal of this work is to establish a bijection between Dyck words and a family of Eulerian digraphs. We do so by providing two algorithms implementing such bijection in bot…
An Analysis of Ruspini Partitions in Gödel Logic
Pietro Codara, Ottavio M. D'Antona, Vincenzo Marra
By a Ruspini partition we mean a finite family of fuzzy sets , , such that for all , where …
Valuations in Gödel Logic, and the Euler Characteristic
Pietro Codara, Ottavio M. D'Antona, Vincenzo Marra
Using the lattice-theoretic version of the Euler characteristic introduced by V. Klee and G.-C. Rota in the Sixties, we define the Euler characteristic of a formula in Gödel logic…
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…
Independent subsets of powers of paths, and Fibonacci cubes
Pietro Codara, Ottavio M. D'Antona
We provide a formula for the number of edges of the Hasse diagram of the independent subsets of the h-th power of a path ordered by inclusion. For h=1 such a value is the number of…
The logical content of triangular bases of fuzzy sets in Łukasiewicz infinite-valued logic
Pietro Codara, Ottavio M. D'Antona, Vincenzo Marra
Continuing to pursue a research direction that we already explored in connection with Gödel-Dummett logic and Ruspini partitions, we show here that Łukasiewicz logic is able to exp…
On the independent subsets of powers of paths and cycles
Pietro Codara, Ottavio M. D'Antona
In the first part of this work we provide a formula for the number of edges of the Hasse diagram of the independent subsets of the h-th power of a path ordered by inclusion. For h=…