Forbidden subsequences and Chebyshev polynomials

Chow, Timothy Y.; West, Julian

doi:10.1016/s0012-365x(98)00384-7

Cited by 64 publications

(85 citation statements)

References 4 publications

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“…Observe that our definition differs slightly from the one used in [B2,MV2]: their layered patterns are exactly the complements of our layered patterns. It was revealed in several recent papers (see [CW,MV1,Kr] and especially [MV2]) that layered restrictions are intimately related to Chebyshev polynomials of the second kind U p cos θ = sin p + 1 θ/ sin θ. Following [MV1], introduce…”

Section: Avoiding a Patternmentioning

confidence: 99%

Restricted 132-Avoiding Permutations

Mansour¹,

Vainshtein²

2001

Advances in Applied Mathematics

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Section: Avoiding a Patternmentioning

confidence: 99%

Restricted 132-Avoiding Permutations

Mansour¹,

Vainshtein²

2001

Advances in Applied Mathematics

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“…Of course, the ij entry of the matrix M k gives this sum for v i and v j . In [5] and [23], the matrix M is called a "transfer matrix". When calculating pgd-vectors for a graph sequence {G n : n = 0, 1, .…”

Section: Polynomial Matrix and Transfer Matrix Methodsmentioning

confidence: 99%

Calculating genus polynomials via string operations and matrices

et al. 2018

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To calculate the genus polynomials for a recursively specifiable sequence of graphs, the set of cellular imbeddings in oriented surfaces for each of the graphs is usually partitioned into imbedding-types. The effects of a recursively applied graph operation τ on each imbedding-type are represented by a production matrix. When the operation τ amounts to constructing the next member of the sequence by attaching a copy of a fixed graph H to the previous member, Stahl called the resulting sequence of graphs an H-linear family. We demonstrate herein how representing the imbedding types by strings and the operation τ by string operations enables us to automate the calculation of the production matrices, a task requiring time proportional to the square of the number of imbedding-types.

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“…Not only in analysis, but in combinatorics, Chebyshev polynomials appear in permutation pattern avoidances [7] and Chebyshev posets, Chebyshev transformations defined by Hetyei which are related to cd-indeices, f -vectors and h-vectors respectively.…”

Section: Conjecture 1 ([5][10])mentioning

confidence: 99%

A Generalization of the Chebyshev Polynomials and Nonrooted Posets

Tomie

2009

International Mathematics Research Notices

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A generalization of Chebyshev polynomials and non rooted posetsMasaya Tomie tomie@math.tsukuba.ac.jpIn this paper we give a generalization of Chebyshev polynomials and using this we describe the Mobius function of the generalized subword order derived from a poset {a 1 , · · · a s , c | a i < c f or i = 1, · · · s}, which contains an affirmative answer for the conjecture by Björner, Sagan and Vatter.(cf,[5] [10])

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Forbidden subsequences and Chebyshev polynomials

Cited by 64 publications

References 4 publications

Restricted 132-Avoiding Permutations

Restricted 132-Avoiding Permutations

Calculating genus polynomials via string operations and matrices

A Generalization of the Chebyshev Polynomials and Nonrooted Posets

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