Daniel YAQUBI, Toufik MANSOUR, Madjid MIRZAVAZIRI

105118

The twelvefold way, the nonintersecting circles problem, and partitions of multisets

Let $n$ be a nonnegative integer and $\mathbb{A}=\{a_1,\ldots,a_k\}$ be a multiset with $k$ positive integers such that $a_1\leqslant\cdots\leqslant a_k$. In this paper, we give a recursive formula for partitions and distinct partitions of positive integer $n$ with respect to a multiset $\mathbb{A}$. We also consider the extension of the twelvefold way. By using this notion, we solve the nonintersecting circles problem, which asks to evaluate the number of ways to draw $n$ nonintersecting circles in the plane regardless of their sizes. The latter also enumerates the number of unlabeled rooted trees with $n+1$ vertices.
Keywords:

Multiset, partitions and distinct partitions, twelvefold way nonintersecting circles problem, rooted trees, Wilf partitions,

PDF
Turkish Journal of Mathematics-Cover
  • ISSN: 1300-0098
  • Yayın Aralığı: 6
  • Yayıncı: TÜBİTAK
Arşiv
Sayıdaki Diğer Makaleler

Xiaomei WU, Xiao YU

The numerical range of matrices over F4

Edoardo BALLICO

İlker Savaş YÜCE

Singly generated invariant subspaces in the Hardy space on the unit ball

Nazım SADIK, Beyaz Başak KOCA

Study on the existence of solutions to two specific types of differential-difference equations

Qiong WANG, Qiongyan WANG

Tuğba Han ŞİMŞEKLER

RT distance and weight distributions of Type 1 constacyclic codes of length $4p^s$ over $frac{F_{p^{mleft[uright]}}}{leftlangle u^arightrangle}$

Hai Q. DINH, Bac Trong NGUYEN, Songsak SRIBOONCHITTA

Exponential stabilization of a neutrally delayed viscoelastic Timoshenko beam

Sebti KERBAL, Nasser Eddine TATAR

Conformal changes of generalized paracontact pseudometric structures

Fereshteh MALEK, Niloufar HOSSEINPOUR KASHANI

The numerical range of matrices over $\mathbb {F}_4$

Edoardo BALLICO