14 citations · 48 across the 14 of their papers we have counts for
14 papers
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…
Characterizing and computing stable models of logic programs: The non-stratified case
Gianpaolo Brignoli, Stefania Costantini, Ottavio D'Antona +1
Stable Logic Programming (SLP) is an emergent, alternative style of logic programming: each solution to a problem is represented by a stable model of a deductive database/function-…
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-…
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=…
Symmetric chain decompositions of B_n and Pi_n
Erensto Damiani, Ottavio D'Antona, Daniel E. Loeb
We review the Green/Kleitman/Leeb interpretation of de Bruijn's symmetric chain decomposition of , and explain how it can be used to find a maximal collection of disj…
Getting results with negative thinking
S. Anelli, Ernesto Damiani, Ottavio D'Antona +1
Given a universe of discourse , a {\em multiset} can be thought of as a function from to the natural numbers . In this paper, we define a {\em hybrid set} to be…