17 research outputs found
Valuations in Nilpotent Minimum Logic
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 characteristic on NM algebras, the algebraic counterpart
of Nilpotent Minimum logic. Then, we introduce a new valuation, a modified
version of the Euler characteristic we call idempotent Euler characteristic. We
show that the new valuation encodes information about the formul{\ae} in NM
propositional logic
On the independent subsets of powers of paths and cycles
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=1 such a value is the number of edges of a
Fibonacci cube. We show that, in general, the number of edges of the diagram is
obtained by convolution of a Fibonacci-like sequence with itself.
In the second part we consider the case of cycles. We evaluate the number of
edges of the Hasse diagram of the independent subsets of the h-th power of a
cycle ordered by inclusion. For h=1, and n>1, such a value is the number of
edges of a Lucas cube.Comment: 9 pages, 4 figure
Eulerian digraphs and Dyck words, a bijection
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 both directions. The connection between Dyck
words and Eulerian digraphs exploits a novel combinatorial structure: a binary
matrix, we call Dyck matrix, representing the cycles of an Eulerian digraph
Making simple proofs simpler
An open partition \pi{} [Cod09a, Cod09b] of a tree T is a partition of the
vertices of T with the property that, for each block B of \pi, the upset of B
is a union of blocks of \pi. This paper deals with the number, NP(n), of open
partitions of the tree, V_n, made of two chains with n points each, that share
the root