https://ajcombinatorics.org/ojs/index.php/AmJC/issue/feed 2026-01-18T21:54:55-05:00 Sudipta Mallik editor@ajcombinatorics.org Open Journal Systems <p>The American Journal of Combinatorics (AmJC) is a double-blind refereed <a href="https://en.wikipedia.org/wiki/Diamond_open_access#/media/File:Open_Access_colours_Venn.svg" target="_blank" rel="noopener">diamond open access</a> online journal. AmJC publishes research articles, notes, and surveys in all branches of combinatorics including graph theory as well as articles related to combinatorics. AmJC was established to support growing research on combinatorics all over the world and to create a free online research publishing platform that is accessible to all. There are <strong>no Article Processing Charges</strong>.</p> <h4><a href="https://portal.issn.org/resource/ISSN/2768-4202" target="_blank" rel="noopener">ISSN 2768-4202</a></h4> <p><a href="https://doaj.org/toc/2768-4202" target="_blank" rel="noopener">Indexed in the Directory of Open Access Journals (DOAJ)</a></p> <p><a href="https://www.oaspa.org/membership/current-members/american-journal-of-combinatorics/" target="_blank" rel="noopener">Member of OASPA</a></p> https://ajcombinatorics.org/ojs/index.php/AmJC/article/view/33 2025-12-24T04:46:30-05:00 Pamela Harris peharris@uwm.edu

<p>Vacillating parking functions are parking functions in which a car only tolerates parking in its preferred spot, in the spot behind its preferred spot, or in the spot ahead of its preferred spot, which they check precisely in that order. Our main result characterizes the possible permutations that arise as parking outcomes from the parking process of nondecreasing vacillating parking functions, which are vacillating parking functions in which every car prefers a spot at least the preference of the previous car. We show that a permutation is the outcome of a nondecreasing vacillating parking function if and only if the permutation is a product of commuting adjacent transpositions. This readily implies that the number of distinct permutations arising as outcomes of nondecreasing vacillating parking functions is a Fibonacci number. We also show that the number of nondecreasing vacillating parking functions that have a fixed outcome consisting of \(k\) commuting adjacent transpositions is always a power of two. We conclude by using these results to give a new formula for the number of nondecreasing vacillating parking functions.</p>

2026-01-18T00:00:00-05:00 Copyright (c) 2026 Pamela Harris https://ajcombinatorics.org/ojs/index.php/AmJC/article/view/32 2025-11-26T16:39:40-05:00 Albert Oloo Nyariaro albertpoly01@gmail.com Isaac Owino Okoth ookoth@maseno.ac.ke Fredrick Oluoch Nyamwala foluoch2000@mu.ac.ke

<pre>Deutsch, Munarin and Rinaldi derived a formula for counting marked plane trees while investigating the enumeration of skew Dyck paths. The formula involves the Catalan numbers, which count plane trees among other classical combinatorial structures. In this paper, we generalize their result by enumerating families of noncrossing trees and recently introduced \(d\)-dimensional plane trees in which certain edges are marked. The resulting formulas are shown to also count: noncrossing trees that allow multi-edges, plane trees in which each internal vertex has outdegree at most 3 and some edges may be marked, and ternary trees in which certain edge type are coloured using two colours. These generalizations provide new combinatorial interpretations and extend the scope of the original enumeration.</pre>

2026-03-18T00:00:00-04:00 Copyright (c) 2026 Albert Oloo Nyariaro, Isaac Owino Okoth, Fredrick Oluoch Nyamwala