Analytic properties of sextet polynomials of hexagonal systems

Li, Guanru; Liu, Lily Li; Wang, Yi

doi:10.1007/s10910-021-01213-x

Cited by 8 publications

(5 citation statements)

References 19 publications

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“…Li et al [27] also gave generating function for the sextet polynomials. They also gave some properties of these polynomials.…”

Section: Preliminariesmentioning

confidence: 99%

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Construction of general forms of ordinary generating functions for more families of numbers and multiple variables polynomials

Şimşek¹

2023

Preprint

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The aim of this paper is to construct general forms of ordinary generating functions for special numbers and polynomials involving Fibonacci type numbers and polynomials, Lucas numbers and polynomials, Chebyshev polynomials, Sextet polynomials, Humbert-type numbers and polynomials, chain and antichain polynomials, rank polynomials of the lattices, length of any alphabet of words, and other graph polynomials. By applying the Euler transform and the Lambert series to these generating functions, many new identities and relations are derived. By using differential equations of these generating functions, some new recurrence relations for these polynomials are found. General Binet's type formulas for these polynomials are given. Finally, some new classes of polynomials and their corresponding certain family of special numbers are investigated with the help of these generating functions.

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“…Li et al [27] also gave generating function for the sextet polynomials. They also gave some properties of these polynomials.…”

Section: Preliminariesmentioning

confidence: 99%

“…Moreover, topological properties of hexagonal systems have many importan applications in various quantum mechanical models of the electronic structure of benzenoid hydrocarbons and also in resonance theory, Huckel molecular orbital theory, Clar's aromatic sextet theory and the theory of conjugated circuits (cf. [6,18,27]).…”

Section: Preliminariesmentioning

confidence: 99%

Construction of general forms of ordinary generating functions for more families of numbers and multiple variables polynomials

Şimşek¹

2023

Preprint

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“…Balasubramanian showed computational symmetry techniques that can be applied to SP [184]. Li et al investigated analytic properties of sextet polynomials of hexagonal systems [185]. A review presenting the SP, Clar polynomial, and Clar-covering polynomial may further complete this enumeration [186].…”

Section: Sextet Polynomialmentioning

confidence: 99%

Counting Polynomials in Chemistry: Past, Present, and Perspectives

Joița,

Tomescu,

Jäntschi

2023

Symmetry

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Counting polynomials find their way into chemical graph theory through quantum chemistry in two ways: as approximate solutions to the Schrödinger equation or by storing information in a mathematical form and trying to find a pattern in the roots of these expressions. Coefficients count how many times a property occurs, and exponents express the extent of the property. They help understand the origin of regularities in the chemistry of specific classes of compounds. Our objective is to accelerate the research of newcomers into chemical graph theory. One problem in understanding these concepts is in the different approaches and notations of each research study; some researchers provide online tools for computing these mathematical concepts, but these need to be maintained for functionality. We take advantage of similar mathematical aspects of 14 such polynomials that merge theoretical chemistry and pure mathematics; give examples, differences, and similarities; and relate them to recent research.

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“…In [17], the recursive relation of the sextet polynomial for several classes of benzenoid systems including pyrene chains was obtained. Recently, zeros of sextet polynomials for pyrene chains were analyzed in [15] and the forcing and anti-forcing polynomials of perfect matchings of pyrene chains were studied in [5]. Note D(R n ) = + G + n when G is the graph as shown in Fig.…”

Section: Pyrene Chainsmentioning

confidence: 99%

“…In [15], the authors studied sextet polynomials of hexagonal systems via generating functions, which motivates us to study the Tutte polynomial of benzenoid systems with recursive structure via generating functions. This is realized by computing the Tutte polynomial of fan-like graph families which are the planar duals of some benzenoid systems with repeated substructures.…”

Section: Introductionmentioning

confidence: 99%