Ars Combinatoria

ISSN 0381-7032 (print), 2817-5204 (online)

Ars Combinatoria is the oldest Canadian Journal of Combinatorics, established in 1976. The journal is dedicated to advancing the field of combinatorial mathematics through the publication of high-quality research papers. From 2024 onward, it publishes four volumes per year in March, June, September and December. Ars Combinatoria has gained recognition and visibility in the academic community and is indexed in renowned databases such as MathSciNet, Zentralblatt, and Scopus. The Scope of the journal includes Graph theory, Design theory, Extremal combinatorics, Enumeration, Algebraic combinatorics, Combinatorial optimization, Ramsey theory, Automorphism groups, Coding theory, Finite geometries, Chemical graph theory but not limited.

Malgorzata Kuchta1, Michal Morayne1, Jaroslaw Niemiec1
1Institute of Mathematics and Computer Science, Wroclaw University of Technology, Wybrzeze Wyspiariskiego 27, 50-370 Wroclaw, POLAND
Abstract:

Let \(T\) be a partially ordered set whose Hasse diagram is a binary tree and let \(T\) possess a unique maximal element \(1_T\). For a natural number \(n\), we compare the number \(A_T^n\) of those chains of length \(n\) in \(T\) that contain \(1_T\) and the number \(B_T^n\) of those chains that do not contain \(1_T\). We show that if the depth of \(T\) is greater or equal to \(2n + [ n \log n ]\) then \(B_T^n > A_T^n\).

Xiangling Zhu1
1Department of Mathematics, JiaYing University 514015, Meizhou, GuangDong, China
Abstract:

The boundedness and compactness of the weighted composition operator from logarithmic Bloch spaces to a class of weighted-type spaces are studied in this paper.

Zhihe Liang1
1Department of Mathematics, Hebei Normal University Shijiazhuang 050016, P. R. China
Abstract:

S.M. Lee proposed the conjecture: for any \(n > 1\) and any permutation \(f\) in \(S(n)\), the permutation graph \(P(P_n, f)\) is graceful. For any integer \(n > 1\), we discuss gracefulness of the permutation graphs \(P(P_n, f)\) when \(f = (123), (n-2, n-1, n), (i, i+1), 1 \leq i \leq n-1, (12)(34)\ldots(2m-1, 2m), 1 \leq m \leq \frac{n}{2}\), and give some general results.

Jianqin Zhou1,2
1Telecommunication School Hangzhou Dianzi University, Hangzhou 310018, China
2Computer Science School Anhui University of Technology, Ma’anshan 243002, China
Abstract:

A double-loop network (DLN) \(G(N;r,s)\) is a digraph with the vertex set \(V = \{0,1,\ldots, N-1\}\) and the edge set \(E=\{v \to v+r \pmod{N} \text{ and } v \to v+s \pmod{N} | v \in V\}\). Let \(D(N;r,s)\) be the diameter of \(G(N;r,s)\) and let us define \(D(N) = \min\{D(N;r,s) | 1 \leq r < s < N \text{ and } \gcd(N,r,s) = 1\}\), \(D_1(N) = \min\{D(N;1,s) | 1 < s 0\)). Coppersmith proved that there exists an infinite family of \(N\) for which the minimum diameter \(D(N) \geq \sqrt{3N} + c(\log N)^{\frac{1}{4}}\), where \(c\) is a constant.

Hikoe Enomoto1, Hajime Matsumura 2
1Department of Mathematics Hiroshima University Higashi-Hiroshima 739-8526, Japan
2Department of Mathematics Keio University Yokohama 223-8522, Japan
Abstract:

In this paper, we consider cycle-partition problems which deal with the case when both vertices and edges are specified and we require that they should belong to different cycles. Minimum degree and degree sum conditions are given, which are best possible.

E. Kilic1, D. Tasci2
1TOBB ECONOMICS AND TECHNOLOGY UNIVERSITY MATHEMATICS DEPARTMENT 06560 ANKARA TURKEY
2Gazt UNIVERSITY, DEPARTMENT OF MATHEMATICS, 06500 ANKARA TURKEY
Abstract:

In this paper, we consider the relationships between the second order linear recurrences and the permanents and determinants of tridiagonal matrices.

Stevo Stevic1
1Mathematical Institute of the Serbian Academy of Science, Knez Mihailova 36/III, 11000 Beograd, Serbia
Abstract:

We correct and improve results from a recent paper by G. Ren and U. Kahler, which characterizes the Bloch, the little Bloch and Besov space of harmonic functions on the unit ball \({B} \subset \mathbb{R}^n\).

Hikoe Enomoto1, Jun Fujisawa2
1Department of Mathematics Hiroshima University Higashi-Hiroshima, 739-8526 Japan
2 Department of Mathematics Keio University Yokohama, 223-8522 Japan
Abstract:

Let \(G\) be a \(2\)-connected graph with maximum degree \(\Delta(G) \geq d\), and let \(x\) and \(z\) be distinct vertices of \(G\). Let \(W\) be a subset of \(V(G) \setminus \{x, z\}\) such that \(|W| \leq d – 1\). Hirohata proved that if \(\max\{d_G(u), d_G(v)\} \geq d\) for every pair of vertices \(u, v \in V(G) \setminus \{x, z\} \cup W\) such that \(d_G(u, v) = 2\), then \(x\) and \(z\) are joined by a path of length at least \(d – |W|\). In this paper, we show that if \(G\) satisfies the conditions of Hirohata’s theorem, then for any given vertex \(y\) such that \(d_G(y) \geq d\), \(x\) and \(z\) are joined by a path of length at least \(d – |W|\) which contains \(y\).

Dan Saracino1, Brian Wynne1
1Colgate University
Abstract:

For any positive integer \(k\), there exists a smallest positive integer \(N\), depending on \(k\), such that every \(2\)-coloring of \(1, 2, \ldots, N\) contains a monochromatic solution of the equation \(x + y + kz = 3w\). Based on computer checks, Robertson and Myers in \([5]\) conjectured values for \(N\) depending on the congruence class of \(k\) (mod \(9\)). In this note, we establish the values of \(N\) and find that in some cases they depend on the congruence class of \(k\) (mod \(27\)).

Simone Severini1
1Department of Computer Science, University of Bristol, U.K.
Abstract:

The support of a matrix \(M\) is the \((0, 1)\)-matrix with \(ij\)-th entry equal to \(1\) if the \(ij\)-th entry of \(M\) is non-zero, and equal to \(0\), otherwise. The digraph whose adjacency matrix is the support of \(M\) is said to be the digraph of \(M\). In this paper, we observe some general properties of digraphs of unitary matrices.

E-mail Alert

Add your e-mail address to receive upcoming issues of Ars Combinatoria.

Special Issues

The Combinatorial Press Editorial Office routinely extends invitations to scholars for the guest editing of Special Issues, focusing on topics of interest to the scientific community. We actively encourage proposals from our readers and authors, directly submitted to us, encompassing subjects within their respective fields of expertise. The Editorial Team, in conjunction with the Editor-in-Chief, will supervise the appointment of Guest Editors and scrutinize Special Issue proposals to ensure content relevance and appropriateness for the journal. To propose a Special Issue, kindly complete all required information for submission;