1. Enumeration of consecutive patterns in flattened Catalan wordsMark Shattuck, 2026, izvirni znanstveni članek Opis: A Catalan word w is said to be flattened if the subsequence of w obtained by taking the first letter of each weakly increasing run is nondecreasing. Let F_n denote the set of flattened Catalan words of length n, which has cardinality (3^{n-1}+1)/2 for all n ≥ 1. In this paper, we consider the distribution of several consecutive patterns on F_n. Indeed, we find explicit formulas for the generating functions of the joint distribution on F_n of several trios of patterns, along with an auxiliary parameter. As special cases of these formulas, we obtain the generating function for the distribution of all consecutive patterns of length two or three. The following equivalences with regard to being identically distributed on F_n arise when comparing the various generating functions and may be explained bijectively: 112 ≈122 and 211≈221≈231. In addition, explicit expressions are found for the total number of occurrences on F_n of each pattern of length two or three as well as for the number of avoiders of each pattern. These results can be obtained as special cases of our more general formulas for the generating functions, but may be explained combinatorially as well, the arguments of which are featured herein.
Ključne besede: flattened Catalan word, pattern avoidance, combinatorial statistic, generating function
Objavljeno v RUP: 23.09.2026; Ogledov: 262; Prenosov: 3
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2. Avoidance of binary patterns by Catalan wordsToufik Mansour, Mark Shattuck, 2026, izvirni znanstveni članek Opis: An integral sequence w_1...w_n such that 1 <= w_{i+1} <= w_{i+1} for all 1 <= i <= n-1 with w_1=1 is known as a Catalan word. Let C_n denote the set of all Catalan words of length n and C_n(τ) the subset of Cn whose members avoid the pattern tau. By a binary pattern, we mean one containing at most two distinct letters. In this paper, we enumerate members of C_n(τ) for several infinite families of binary patterns. As a consequence of our results, we obtain generating function formulas for the sequence |C_n(τ)| for n >= 1 for all binary patterns of length four. We also provide bijective proofs of two general Wilf equivalences, namely, that the cardinality of the avoidance class Cn(σ) for either σ=1^a21^b or σ=2^a12^b is independent of a and b once a+b has been specified.
Ključne besede: Catalan word, pattern avoidance, combinatorial statistic, generating function
Objavljeno v RUP: 18.09.2026; Ogledov: 296; Prenosov: 8
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3. Mutually avoiding Eulerian circuitsGrahame Erskine, Terry S. Griggs, Robert Lewis, James Tuite, 2026, izvirni znanstveni članek Opis: Two Eulerian circuits, both starting and ending at the same vertex, are avoiding if at every other point of the circuits they are at least distance 2 apart. An Eulerian graph which admits two such avoiding circuits starting from any vertex is said to be doubly Eulerian. The motivation for this definition is that the extremal Eulerian graphs, i.e. the complete graphs on an odd number of vertices and the cycles, are not doubly Eulerian. We prove results about doubly Eulerian graphs and identify those that are the “densest” and “sparsest” in terms of the number of edges.
Ključne besede: Eulerian circuit, avoidance
Objavljeno v RUP: 20.08.2026; Ogledov: 353; Prenosov: 12
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4. Knowledge avoidance – consistency, taxonomy, and etiologyTomaž Grušovnik, 2025, izvirni znanstveni članek Opis: Often, our reluctance to accept new ideas is the obstacle to advancing knowledge. This reluctance also plays an important role in unethical behavior. Yet, despite being widely recognized as a major factor in moral misconduct across the ethical spectrum, knowledge avoidance is plagued by a lack of clarity about the precise nature and characteristics of the epistemic phenomena it encompasses. First, these phenomena appear to be contradictory, since avoidance usually requires knowledge of what is to be avoided, and thus avoidance of knowledge seems impossible. Second, knowledge avoidance seems to be an umbrella term that encompasses a variety of different doxastic states. And third, the reasons and motivations for knowledge avoidance seem to encompass biological factors as well as ontological and psychological aspects. Drawing on both traditional and contemporary philosophical literature, the present paper aims to shed light on all these faces of knowledge avoidance by exploring problems related to its consistency, taxonomy, and etiology. The essay concludes with an examination of the moral dimensions of these phenomena. It explores the problem of responsibility and culpability, and even the potential benefits of knowledge avoidance.
Ključne besede: knowledge avoidance, willful ignorance, denialism, biased belief formation, culpability
Objavljeno v RUP: 16.06.2025; Ogledov: 1525; Prenosov: 22
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5. Perceived threat of COVID-19 and future travel avoidance : results from an early convenient sample in SloveniaMaja Turnšek, Boštjan Brumen, Marjetka Rangus, Mitja Gorenak, Janez Mekinc, Tanja Lešnik Štuhec, 2020, izvirni znanstveni članek Opis: The present study provides a snapshot of Slovenian tourists' perceptions in a historically unique point of time - the early days of the covid-19-related lockdown. Based on an online survey performed in March and April 2020 the study provides first insights into Slovenian tourists% perceived threats of covid-19 on two dimensions: severity and susceptibility; how this depends on their demography and past travel experience and what, in this specific point in time, they think about future travel avoidance. The results have shown that age affects the two measured dimensions of perceived threat and future travel avoidance, but only with women. Furthermore, people who have travelled the most in the past express the least likelihood of avoidance to travel due to the covid -19 pandemic. Those who are more educated, on the other hand, perceive higher risk, yet education has no role in their expressed future travel avoidance. The results, moreover, show that the moral obligation towards taking care of others might be a highly important element in the success factor of covid-19 measures and thus future appeals by the tourism industry. Finally, the results show that we cannot easily predict how the general population will behave regarding their future travel avoidance since the opinions are not polarised in the extremes. This does indicate, however, that tourists will be susceptible to the context-specific factors of future travel decisions, such as assurances of health safety provided by the tourism industry.
Ključne besede: COVID-19, tourism, health threat perception, future travel avoidance, fear appeals
Objavljeno v RUP: 14.12.2020; Ogledov: 3838; Prenosov: 70
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