Results 51 to 60 of about 93 (68)

The permutation class Av(4213,2143) [PDF]

Discrete Mathematics & Theoretical Computer Science, 2017
We determine the structure of permutations avoiding the patterns 4213 and 2143. Each such permutation consists of the skew sum of a sequence of plane trees, together with an increasing sequence of points above and an increasing sequence of points to its ...
David Bevan
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Proofs of Conjectures about Pattern-Avoiding Linear Extensions [PDF]

Discrete Mathematics & Theoretical Computer Science, 2019
After fixing a canonical ordering (or labeling) of the elements of a finite poset, one can associate each linear extension of the poset with a permutation.
Colin Defant
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The 26 Wilf-equivalence classes of length five quasi-consecutive patterns [PDF]

Discrete Mathematics & Theoretical Computer Science, 2018
We present two families of Wilf-equivalences for consecutive and quasi-consecutive vincular patterns. These give new proofs of the classification of consecutive patterns of length $4$ and $5$.
Evan Chen, Shyam Narayanan
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Key-avoidance for alternating sign matrices [PDF]

Discrete Mathematics & Theoretical Computer Science
We initiate a systematic study of key-avoidance on alternating sign matrices (ASMs) defined via pattern-avoidance on an associated permutation called the \emph{key} of an ASM.
Mathilde Bouvel, Rebecca Smith, Jessica Striker   +2 more
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Convexity of tableau sets for type A Demazure characters (key polynomials), parabolic Catalan numbers [PDF]

Discrete Mathematics & Theoretical Computer Science, 2018
This is the first of three papers that develop structures which are counted by a "parabolic" generalization of Catalan numbers. Fix a subset R of {1,..,n-1}. Consider the ordered partitions of {1,..,n} whose block sizes are determined by R. These are the
Robert A. Proctor, Matthew J. Willis
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Classical pattern distributions in $\mathcal{S}_{n}(132)$ and $\mathcal{S}_{n}(123)$ [PDF]

Discrete Mathematics & Theoretical Computer Science, 2019
Classical pattern avoidance and occurrence are well studied in the symmetric group $\mathcal{S}_{n}$. In this paper, we provide explicit recurrence relations to the generating functions counting the number of classical pattern occurrence in the set of ...
Dun Qiu, Jeffrey Remmel
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Distribution of sets of descent tops and descent bottoms on restricted permutations [PDF]

Discrete Mathematics & Theoretical Computer Science
In this note, we prove some and conjecture other results regarding the distribution of descent top and descent bottom sets on some pattern-avoiding permutations.
Alexander Burstein
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K-Orbit closures and Hessenberg varieties

Forum of Mathematics, Sigma
This article explores the relationship between Hessenberg varieties associated with semisimple operators with two eigenvalues and orbit closures of a spherical subgroup of the general linear group.
Mahir Bilen Can, Martha Precup, John Shareshian, Özlem Uğurlu   +3 more
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Involution factorizations of Ewens random permutations [PDF]

Discrete Mathematics & Theoretical Computer Science
An involution is a bijection that is its own inverse. Given a permutation $σ$ of $[n],$ let $\mathsf{invol}(σ)$ denote the number of ways $σ$ can be expressed as a composition of two involutions of $[n].$ We prove that the statistic $\mathsf{invol}$ is ...
Charles Burnette
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On Matrices with Bidimensional Fibonacci Numbers

Annales Mathematicae Silesianae
In this paper, the bidimensional extensions of the Fibonacci numbers are explored, along with a detailed examination of their properties, characteristics, and some identities.
Costa Eudes Antonio, Catarino Paula M.M.C.   +1 more
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