Strict unimodality of plucking polynomials of rooted trees

Zhiyun Cheng; Sujoy Mukherjee; Józef H. Przytycki; Xiao Wang; Seung Yeop Yang

doi:10.1142/S0218216518410092

Strict unimodality of plucking polynomials of rooted trees

Zhiyun Cheng, Sujoy Mukherjee, Józef H. Przytycki, Xiao Wang, Seung Yeop Yang

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

We classify rooted trees which have strictly unimodal plucking polynomials (q-polynomials). We also give criteria for a trapezoidal shape of a plucking polynomial. We generalize results of Pak and Panova on strict unimodality of q-binomial coefficients.

Original language	English
Article number	1841009
Journal	Journal of Knot Theory and its Ramifications
Volume	27
Issue number	7
DOIs	https://doi.org/10.1142/S0218216518410092
State	Published - 1 Jun 2018

Keywords

Gaussian polynomial
Plucking polynomial
q-binomial coefficients
rooted tree
strict unimodality

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10.1142/S0218216518410092

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title = "Strict unimodality of plucking polynomials of rooted trees",

abstract = "We classify rooted trees which have strictly unimodal plucking polynomials (q-polynomials). We also give criteria for a trapezoidal shape of a plucking polynomial. We generalize results of Pak and Panova on strict unimodality of q-binomial coefficients.",

keywords = "Gaussian polynomial, Plucking polynomial, q-binomial coefficients, rooted tree, strict unimodality",

author = "Zhiyun Cheng and Sujoy Mukherjee and Przytycki, \{J{\'o}zef H.\} and Xiao Wang and Yang, \{Seung Yeop\}",

note = "Publisher Copyright: {\textcopyright} 2018 World Scientific Publishing Company.",

year = "2018",

month = jun,

day = "1",

doi = "10.1142/S0218216518410092",

language = "English",

volume = "27",

journal = "Journal of Knot Theory and its Ramifications",

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T1 - Strict unimodality of plucking polynomials of rooted trees

AU - Cheng, Zhiyun

AU - Mukherjee, Sujoy

AU - Przytycki, Józef H.

AU - Wang, Xiao

AU - Yang, Seung Yeop

PY - 2018/6/1

Y1 - 2018/6/1

N2 - We classify rooted trees which have strictly unimodal plucking polynomials (q-polynomials). We also give criteria for a trapezoidal shape of a plucking polynomial. We generalize results of Pak and Panova on strict unimodality of q-binomial coefficients.

AB - We classify rooted trees which have strictly unimodal plucking polynomials (q-polynomials). We also give criteria for a trapezoidal shape of a plucking polynomial. We generalize results of Pak and Panova on strict unimodality of q-binomial coefficients.

KW - Gaussian polynomial

KW - Plucking polynomial

KW - q-binomial coefficients

KW - rooted tree

KW - strict unimodality

UR - https://www.scopus.com/pages/publications/85046782473

U2 - 10.1142/S0218216518410092

DO - 10.1142/S0218216518410092

M3 - Article

AN - SCOPUS:85046782473

SN - 0218-2165

VL - 27

JO - Journal of Knot Theory and its Ramifications

JF - Journal of Knot Theory and its Ramifications

IS - 7

M1 - 1841009

ER -

Strict unimodality of plucking polynomials of rooted trees

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Keywords

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