Results 41 to 50 of about 122,748 (264)
Pattern Avoidance in Partial Permutations [PDF]
The Electronic Journal of Combinatorics, 2011 Motivated by the concept of partial words, we introduce an analogous concept of partial permutations. A partial permutation of length $n$ with $k$ holes is a sequence of symbols $\pi=\pi_1\pi_2\dotsb\pi_n$ in which each of the symbols from the set $\{1,2,\dotsc,n-k\}$ appears exactly once, while the remaining $k$ symbols of $\pi$ are "holes".
Claesson, Anders +3 more
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Pediatric Blood &Cancer, EarlyView.ABSTRACT Background Central nervous system (CNS) neuroblastoma, FOXR2‐activated, is a recently recognized entity in the WHO CNS5 classification, defined by activation of the FOXR2 transcription factor and unique histopathological features. This review synthesizes available literature and pooled clinical data, providing insight into demographics ...
Sudarshawn Damodharan +1 more
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Classification of bijections between 321- and 132-avoiding permutations [PDF]
Discrete Mathematics & Theoretical Computer Science, 2008 It is well-known, and was first established by Knuth in 1969, that the number of 321-avoiding permutations is equal to that of 132-avoiding permutations. In the literature one can find many subsequent bijective proofs confirming this fact.
Anders Claesson, Sergey Kitaev
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Discrete Mathematics, 2007 The paper studies colorings of graphs avoiding certain patterns on paths. Let \(X\) be a set of variables and let \(p=x_1x_2\dots x_r\) (with \(x_i\in X\)) be a pattern, i.e. any sequence of the variables with repetition allowed. A finite sequence \(s\) is said to match the pattern \(p\), if \(s\) can be divided into non-empty blocks \(s=B_1B_2\dots ...
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Pediatric Blood &Cancer, EarlyView.ABSTRACT Introduction The use of herbal medical preparation (HMP) is rising among pediatric oncology patients, often to manage treatment‐related symptoms. Their effectiveness remains uncertain, and the risk of herb–drug interactions is underestimated.
Orianne Mahot +6 more
wiley +1 more source
Pattern avoidance in parking functions [PDF]
Enumerative Combinatorics and Applications, 2023 Ayomikun Adeniran, Lara Pudwell
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Permutation patterns, Stanley symmetric functions, and the Edelman-Greene correspondence [PDF]
Discrete Mathematics & Theoretical Computer Science, 2013 Generalizing the notion of a vexillary permutation, we introduce a filtration of $S_{\infty}$ by the number of Edelman-Greene tableaux of a permutation, and show that each filtration level is characterized by avoiding a finite set of patterns.
Sara Billey, Brendan Pawlowski
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Pediatric Blood &Cancer, EarlyView.ABSTRACT Pediatric radiation therapy presents unique challenges compared to adult treatments, including those of immobilization, potential need for sedation, and the critical importance of accurate, reproducible positioning. Additionally, heightened attention to imaging doses is necessary to minimize long‐term toxicity in survivors.
Parham Alaei +17 more
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Rational smoothness and affine Schubert varieties of type A [PDF]
Discrete Mathematics & Theoretical Computer Science, 2011 The study of Schubert varieties in G/B has led to numerous advances in algebraic combinatorics and algebraic geometry. These varieties are indexed by elements of the corresponding Weyl group, an affine Weyl group, or one of their parabolic quotients ...
Sara Billey, Andrew Crites
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Alternating, Pattern-Avoiding Permutations [PDF]
The Electronic Journal of Combinatorics, 2009 We study the problem of counting alternating permutations avoiding collections of permutation patterns including $132$. We construct a bijection between the set $S_n(132)$ of $132$-avoiding permutations and the set $A_{2n + 1}(132)$ of alternating, $132$-avoiding permutations. For every set $p_1, \ldots, p_k$ of patterns and certain related patterns $
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