8 research outputs found
ALGORITMA PEMBANGKITAN MENGGUNAKAN POHON
Pembangkitan secara lengkap objek-objek dari kelas kombinatorial tertentu adalah mencari cara atau metode atau algoritma untuk mencacah (list, enumerate) semua objek dalam urutan tertentu tanpa pengulangan dan tidak melewatkan satu objek pun. Salah satu pendekatan dalam membangkitkan objek kombinatorial secara lengkap adalah dengan pohon pembangkit. Pohon pembangkit adalah suatu sistem yang mempunyai akar dan cabang-cabangnya yang dapat direpresentasikan dalam aturan yang dikenal dengan nama aturan suksesi. Pendekatan ini banyak digunakan karena dengan aturan suksesi dapat diterjemahkan kedalam bentuk-bentuk lain seperti operator linier pada polinomial dengan satu variabel, perkalian matriks, atau kode tertentu seperti kode Gray. Dari pohon pembangkit dapat pula dimungkinkan suatu algoritma pembangkitan acak. Makalah membahas pohon pembangkit dan aplikasinya pada objek kombinatorial untai Fibonacci, permutasi dan permutasi dengan siklus
Pembangkitan Permutation dengan Siklus
Makalah ini membahas pembangkitan lengkap objek kombinatorial permutasi khususnya permutasi n dengan satu siklus dengan panjang n. Metode yang akan digunakan dalam pembangkitan permutasi dengan memperhatikan siklus tersebut menggunakan pendekata
PEMBM GKITAl"l PERMUTATION DENGAN SIKLUS
Makalah ini membahas pembangkitan leng\c:ap objek kombinatorial pennutasi khususnya
pennutasi n dengan satu siklus dengan panjang n. Metode yang akan digunakan dalam pembangkitan
pennutasi dengan memperharikan siklus tersebut menggunakan pendekatan pohon pembangkit atau
metode ECO (enumerating combinatorial objects). Dalam metode ini setiap objek diperoleh dati objek
yang lebih kecil dengan melakukan ekspansi lokal, Seringkali ekspansi lokal tersebut sangat teratur dan
dapat dijelaskan dalamamran suksesi, Metode ECO ini telah ditunjukkan efektif untuk beberapa struktur
kombinatorik. Efekrif dalam pembangkitan kombinatorik berarti: waktu untuk menghasilkan (running
rime) sebanding dengan banyaknya objek yang dihasilkan, yang merupakan syarat penring dalam
merancang algoritma pembangkitan obiek kombinatorial
Note on Ward-Horadam H(x) - binomials' recurrences and related interpretations, II
We deliver here second new recurrence formula,
were array is appointed by sequence of
functions which in predominantly considered cases where chosen to be
polynomials . Secondly, we supply a review of selected related combinatorial
interpretations of generalized binomial coefficients. We then propose also a
kind of transfer of interpretation of coefficients onto
coefficients interpretations thus bringing us back to
and Donald Ervin Knuth relevant investigation decades
ago.Comment: 57 pages, 8 figure
Enumeration of polyominoes defined in terms of pattern avoidance or convexity constraints
In this thesis, we consider the problem of characterizing and enumerating
sets of polyominoes described in terms of some constraints, defined either by
convexity or by pattern containment. We are interested in a well known subclass
of convex polyominoes, the k-convex polyominoes for which the enumeration
according to the semi-perimeter is known only for k=1,2. We obtain, from a
recursive decomposition, the generating function of the class of k-convex
parallelogram polyominoes, which turns out to be rational. Noting that this
generating function can be expressed in terms of the Fibonacci polynomials, we
describe a bijection between the class of k-parallelogram polyominoes and the
class of planted planar trees having height less than k+3. In the second part
of the thesis we examine the notion of pattern avoidance, which has been
extensively studied for permutations. We introduce the concept of pattern
avoidance in the context of matrices, more precisely permutation matrices and
polyomino matrices. We present definitions analogous to those given for
permutations and in particular we define polyomino classes, i.e. sets downward
closed with respect to the containment relation. So, the study of the old and
new properties of the redefined sets of objects has not only become
interesting, but it has also suggested the study of the associated poset. In
both approaches our results can be used to treat open problems related to
polyominoes as well as other combinatorial objects.Comment: PhD thesi
Enumeration of convex polyominoes using the ECO method
International audienceECO is a method for the enumeration of classes of combinatorial objects based on recursive constructions of such classes. In the first part of this paper we present a construction for the class of convex polyominoes based on the ECO method. Then we translate this construction into a succession rule. The final goal of the paper is to determine the generating function of convex polyominoes according to the semi-perimeter, and it is achieved by applying an idea introduced in [11]
Enumeration of convex polyominoes using the ECO method
ECO is a method for the enumeration of classes of combinatorial objects based on recursive constructions of such classes. In the first part of this paper we present a construction for the class of convex polyominoes based on the ECO method. Then we translate this construction into a succession rule. The final goal of the paper is to determine the generating function of convex polyominoes according to the semi-perimeter, and it is achieved by applying an idea introduced in [11]
Enumeration of convex polyominoes using the ECO method
ECO is a method for the enumeration of classes of combinatorial objects based on recursive constructions of such classes. In the first part of this paper we present a construction for the class of convex polyominoes based on the ECO method. Then we translate this construction into a succession rule. The final goal of the paper is to determine the generating function of convex polyominoes according to the semi-perimeter, and it is achieved by applying an idea introduced in [11]