Congressus Numerantium

ISSN: 0384-9864

Congressus Numerantium, established in 1970, is one of the oldest international journals devoted to high-quality research in combinatorics and related areas. Over the decades, it has published numerous fully refereed research papers as well as conference proceedings from prestigious international meetings, making it a cornerstone of the combinatorics community.
Open Access: The journal now follows the Diamond Open Access model—completely free for both authors and readers, with no APCs. 
Publication Frequency: From 2024 onward, Congressus Numerantium publishes two volumes annually—released in June and December
Scope: The journal welcomes original research papers and survey articles in pure and applied combinatorics. It also invites special issues dedicated to conferences, workshops, or selected topics of current interest, carrying forward its tradition of serving the global combinatorial mathematics community.
Indexing & Abstracting: Indexed in MathSciNet and zbMATH, ensuring strong visibility and recognition in the international mathematical sciences community.
Rapid Publication: Manuscripts are handled efficiently, with accepted papers prepared and published promptly in the upcoming issue to ensure timely dissemination of research.
Print & Online Editions: Congressus Numerantium is published in both print and online formats.

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Ternary Strings and the Pell Numbers

Ralph P. Grimaldi1
1Mathematics Department Rose-Hulman Institute of Technology Terre Haute, Indiana 47803 US.A.
Abstract:

For \( n \geq 1 \), let \( a_n \) count the number of strings \( s_1 s_2 s_3 \ldots s_n \), where
(i) \( s_1 = 0 \);
(ii) \( s_i \in \{0, 1, 2\} \) for \( 2 \leq i \leq n \);
(iii) \( |s_i – s_{i-1}| \leq 1 \) for \( 2 \leq i \leq n \).

Then \( a_1 = 1 \), \( a_2 = 2 \), \( a_3 = 5 \), \( a_4 = 12 \), and \( a_5 = 29 \).

In general, for \( n \geq 3 \), \( a_n = 2a_{n-1} + a_{n-2} \), and \( a_n \) equals \( P_n \), the \( n \)th \emph{Pell} number.

For these \( P_n \) strings of length \( n \), we count
(i) The number of occurrences of each symbol \( 0, 1, 2 \);
(ii) The number of times each symbol \( 0, 1, 2 \) occurs in an even or odd position;
(iii) The number of levels, rises, and descents within the strings;
(iv) The number of runs that occur within the strings;
(v) The sum of all strings considered as base \( 3 \) integers;
(vi) The number of inversions and coinversions within the strings; and
(vii) The sum of the major indices for the strings.

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The pseudograph threshold number \(\pi(r, s, a, t)\)

A. J. W. Hilton, A. Rajkumar
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H-Decompositions of Generalized Johnson Graphs

Braxton Carrigan, Aaron Clark, James Hammer
Abstract:

A family of graphs, called Generalized Johnson graphs, provides an abstraction of both Kneser and Johnson graphs.
Given the symmetric nature of Generalized Johnson graphs, we provide various decompositions of these graphs and demonstrate non-trivial instances of the impossibility of decomposing such graphs into triples.

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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;
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