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1
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Quasi-particle fermionic formulas for (k, 3)-admissible configurations

100%
Jerković M., Primc M.
Open Mathematics
|
2012
|
tom 10
|
nr 2
703-721
EN
We construct new monomial quasi-particle bases of Feigin-Stoyanovsky type subspaces for the affine Lie algebra sl(3;ℂ)∧ from which the known fermionic-type formulas for (k, 3)-admissible configurations follow naturally. In the proof we use vertex operator algebra relations for standard modules and coefficients of intertwining operators.
2
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Some new transformations for Bailey pairs and WP-Bailey pairs

100%
Mc Laughlin J.
Open Mathematics
|
2010
|
tom 8
|
nr 3
474-487
EN
We derive several new transformations relating WP-Bailey pairs. We also consider the corresponding transformations relating standard Bailey pairs, and as a consequence, derive some quite general expansions for products of theta functions which can also be expressed as certain types of Lambert series.
3
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Fourier series of functions involving higher-order ordered Bell polynomials

100%
Kim T., Kim D. S., Jang G.-W., Jang L. C.
Open Mathematics
|
2017
|
tom 15
|
nr 1
1606-1617
EN
In 1859, Cayley introduced the ordered Bell numbers which have been used in many problems in number theory and enumerative combinatorics. The ordered Bell polynomials were defined as a natural companion to the ordered Bell numbers (also known as the preferred arrangement numbers). In this paper, we study Fourier series of functions related to higher-order ordered Bell polynomials and derive their Fourier series expansions. In addition, we express each of them in terms of Bernoulli functions.
4
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A note on the determinant of a Toeplitz-Hessenberg matrix

100%
Merca M.
Special Matrices
|
2013
|
tom 1
10-16
EN
The nth-order determinant of a Toeplitz-Hessenberg matrix is expressed as a sum over the integer partitions of n. Many combinatorial identities involving integer partitions and multinomial coefficients can be generated using this formula.
5
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Combinatorial bases of modules for affine Lie algebra B 2(1)

100%
Primc M.
Open Mathematics
|
2013
|
tom 11
|
nr 2
197-225
EN
We construct bases of standard (i.e. integrable highest weight) modules L(Λ) for affine Lie algebra of type B 2(1) consisting of semi-infinite monomials. The main technical ingredient is a construction of monomial bases for Feigin-Stoyanovsky type subspaces W(Λ) of L(Λ) by using simple currents and intertwining operators in vertex operator algebra theory. By coincidence W(kΛ0) for B 2(1) and the integrable highest weight module L(kΛ0) for A 1(1) have the same parametrization of combinatorial bases and the same presentation P/I.
6
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Differential equations associated with generalized Bell polynomials and their zeros

84%
Ryoo S. C.
Open Mathematics
|
2016
|
tom 14
|
nr 1
807-815
EN
In this paper, we study differential equations arising from the generating functions of the generalized Bell polynomials.We give explicit identities for the generalized Bell polynomials. Finally, we investigate the zeros of the generalized Bell polynomials by using numerical simulations.
7
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Fully degenerate poly-Bernoulli numbers and polynomials

84%
Kim T., Kim D. S., Seo J.-J.
Open Mathematics
|
2016
|
tom 14
|
nr 1
545-556
EN
In this paper, we introduce the new fully degenerate poly-Bernoulli numbers and polynomials and inverstigate some properties of these polynomials and numbers. From our properties, we derive some identities for the fully degenerate poly-Bernoulli numbers and polynomials.
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