Search results for "binary [neutron star]"
showing 10 items of 544 documents
Combinatorial aspects of L-convex polyominoes
2007
We consider the class of L-convex polyominoes, i.e. those polyominoes in which any two cells can be connected with an ''L'' shaped path in one of its four cyclic orientations. The paper proves bijectively that the number f"n of L-convex polyominoes with perimeter 2(n+2) satisfies the linear recurrence relation f"n"+"2=4f"n"+"1-2f"n, by first establishing a recurrence of the same form for the cardinality of the ''2-compositions'' of a natural number n, a simple generalization of the ordinary compositions of n. Then, such 2-compositions are studied and bijectively related to certain words of a regular language over four letters which is in turn bijectively related to L-convex polyominoes. In …
Enumerating the Walecki-Type Hamiltonian Cycle Systems
2017
Let Kv be the complete graph on v vertices. A Hamiltonian cycle system of odd order v (briefly HCS(v)) is a set of Hamiltonian cycles of Kv whose edges partition the edge set of Kv. By means of a slight modification of the famous HCS(4n+1) of Walecki, we obtain 2n pairwise distinct HCS(4n+1) and we enumerate them up to isomorphism proving that this is equivalent to count the number of binary bracelets of length n, i.e. the orbits of Dn, the dihedral group of order 2n, acting on binary n-tuples.
On the use of relational expressions in the design of efficient algorithms
2005
Relational expressions have finite binary relations as arguments and the operations are composition (·), closure (*), inverse (−1), and union (U). The efficient computation of the relation denoted by a relational expression is considered, and a tight bound is established on the complexity of the algorithm suggested by Hunt, Szymanski and Ullman. The result implies a unified method for deriving efficient algorithms for many problems in parsing. For example, optimal algorithms are derived for strong LL(1) and strong LL(2) parser construction and an efficient polynomialtime algorithm is derived for determining the inessential error entries in an LR(1) parsing table.
Balancing and clustering of words in the Burrows–Wheeler transform
2011
AbstractCompression algorithms based on Burrows–Wheeler transform (BWT) take advantage of the fact that the word output of BWT shows a local similarity and then turns out to be highly compressible. The aim of the present paper is to study such “clustering effect” by using notions and methods from Combinatorics on Words.The notion of balance of a word plays a central role in our investigation. Empirical observations suggest that balance is actually the combinatorial property of input word that ensure optimal BWT compression. Moreover, it is reasonable to assume that the more balanced the input word is, the more local similarity we have after BWT (and therefore the better the compression is).…
A Motzkin filter in the Tamari lattice
2015
The Tamari lattice of order n can be defined on the set T n of binary trees endowed with the partial order relation induced by the well-known rotation transformation. In this paper, we restrict our attention to the subset M n of Motzkin trees. This set appears as a filter of the Tamari lattice. We prove that its diameter is 2 n - 5 and that its radius is n - 2 . Enumeration results are given for join and meet irreducible elements, minimal elements and coverings. The set M n endowed with an order relation based on a restricted rotation is then isomorphic to a ranked join-semilattice recently defined in Baril and Pallo (2014). As a consequence, we deduce an upper bound for the rotation distan…
Matchings in three Catalan lattices
2003
In this note we consider a series of lattices that are enumerated by the well-known Catalan numbers. For each of these lattices, we exhibit a matching in a constructive way.
Generating binary trees by Glivenko classes on Tamari lattices
2003
Using algebraic-theoretic results, we give an algorithm for generating binary trees within Glivenko classes in Tamari lattices. Tamari lattices are lattices of binary trees endowed by the well-known rotation transformation.
Ordering and Convex Polyominoes
2005
We introduce a partial order on pictures (matrices), denoted by ≼ that extends to two dimensions the subword ordering on words. We investigate properties of special families of discrete sets (corresponding to {0,1}-matrices) with respect to this partial order. In particular we consider the families of polyominoes and convex polyominoes and the family, recently introduced by the authors, of L-convex polyominoes. In the first part of the paper we study the closure properties of such families with respect to the order. In particular we obtain a new characterization of L-convex polyominoes: a discrete set P is a L-convex polyomino if and only if all the elements Q≼P are polyominoes. In the seco…
The Rotation χ-Lattice of Ternary Trees
2001
This paper generalizes to k-ary trees the well-known rotation transformation on binary trees. For brevity, only the ternary case is developped. The rotation on ternary trees is characterized using some codings of trees. Although the corresponding poset is not a lattice, we show that it is a χ-lattice in the sense of Leutola–Nieminen. Efficient algorithms are exhibited to compute meets and joins choosen in a particular way.
A fractal set from the binary reflected Gray code
2005
The permutation associated with the decimal expression of the binary reflected Gray code with $N$ bits is considered. Its cycle structure is studied. Considered as a set of points, its self-similarity is pointed out. As a fractal, it is shown to be the attractor of a IFS. For large values of $N$ the set is examined from the point of view of time series analysis