Publications

2022

[Banerjee]

Hook Type enumeration and parity of parts in partitions

K. Banerjee, M. G. Dastidar

Research Institute for Symbolic Computation, JKU, Linz. Technical report no. RISC6596, 2022. [pdf]

[bib]

@techreport{RISC6596,
author = {K. Banerjee and M. G. Dastidar},
title = {{Hook Type enumeration and parity of parts in partitions}},
language = {english},
abstract = {This paper is devoted to study an association between hook type enumeration and counting integer partitions subject to parity of its parts. We shall primarily focus on a result of Andrews in two possible direction. First, we confirm a conjecture of Rubey and secondly, we extend the theorem of Andrews in a more general set up. },
number = {RISC6596},
year = {2022},
institution = {Research Institute for Symbolic Computation, JKU, Linz},
length = {8}
}

[Banerjee]

Hook type tableaux and partition identities

K. Banerjee, M. G. Dastidar

Research Institute for Symbolic Computation, JKU, Linz. Technical report no. RISC6597, 2022. [pdf]

[bib]

@techreport{RISC6597,
author = {K. Banerjee and M. G. Dastidar},
title = {{Hook type tableaux and partition identities}},
language = {english},
abstract = {In this paper we exhibit the box-stacking principle (BSP) in conjunction with Young diagrams to prove generalizations of Stanley's and Elder's theorems without even the use of partition statistics in general. We primarily focus on to study Stanley's theorem in color partition context.},
number = {RISC6597},
year = {2022},
institution = {Research Institute for Symbolic Computation, JKU, Linz},
length = {13}
}

[Banerjee]

Positivity of the second shifted difference of partitions and overpartitions: a combinatorial approach

Koustav Banerjee

Research Institute for Symbolic Computation, JKU, Linz. Technical report no. RISC6592, 2022. [pdf]

[bib]

@techreport{RISC6592,
author = {Koustav Banerjee},
title = {{Positivity of the second shifted difference of partitions and overpartitions: a combinatorial approach}},
language = {english},
number = {RISC6592},
year = {2022},
institution = {Research Institute for Symbolic Computation, JKU, Linz},
length = {5}
}

[Banerjee]

Ramanujan's theta functions and parity of parts and cranks of partitions

K. Banerjee, M. G. Dastidar

Research Institute for Symbolic Computation, JKU, Linz. Technical report no. RISC6595, 2022. [pdf]

[bib]

@techreport{RISC6595,
author = {K. Banerjee and M. G. Dastidar},
title = {{Ramanujan's theta functions and parity of parts and cranks of partitions}},
language = {english},
abstract = {In this paper we explore intricate connections between Ramanujan's theta functions and a class of partition functions defined by the nature of the parity of their parts. This consequently leads us to the parity analysis of the crank of a partition and its correlation to the number of partitions with odd number of parts, self-conjugate partitions, and also with Durfee squares and Frobenius symbols.},
number = {RISC6595},
year = {2022},
institution = {Research Institute for Symbolic Computation, JKU, Linz},
length = {13}
}

[Banerjee]

Inequalities for the partition function arising from truncated theta series

K. Banerjee, M. G. Dastidar

Research Institute for Symbolic Computation, JKU, Linz. Technical report no. RISC6622, 2022. [pdf]

[bib]

@techreport{RISC6622,
author = {K. Banerjee and M. G. Dastidar},
title = {{Inequalities for the partition function arising from truncated theta series}},
language = {english},
number = {RISC6622},
year = {2022},
institution = {Research Institute for Symbolic Computation, JKU, Linz},
length = {12}
}

[Banerjee]

Parity biases in partitions and restricted partitions

Banerjee Koustav, Bhattacharjee Sreerupa, Dastidar Manosij Ghosh, Mahanta Pankaj Jyoti, Saikia Manjil P

European Journal of Combinatorics 103, pp. 103522-103522. 2022. Elsevier, ISSN 0195-6698. [pdf]

[bib]

@article{RISC6606,
author = {Banerjee Koustav and Bhattacharjee Sreerupa and Dastidar Manosij Ghosh and Mahanta Pankaj Jyoti and Saikia Manjil P},
title = {{Parity biases in partitions and restricted partitions}},
language = {english},
journal = {European Journal of Combinatorics},
volume = {103},
pages = {103522--103522},
publisher = {Elsevier},
isbn_issn = {ISSN 0195-6698},
year = {2022},
refereed = {yes},
length = {19}
}

[Banerjee]

New inequalities for p(n) and log p(n)

K. Banerjee, P. Paule, C. S. Radu, W. H. Zeng

Research Institute for Symbolic Computation, JKU, Linz. Technical report no. RISC6607, 2022. [pdf]

[bib]

@techreport{RISC6607,
author = {K. Banerjee and P. Paule and C. S. Radu and W. H. Zeng},
title = {{New inequalities for p(n) and log p(n)}},
language = {english},
number = {RISC6607},
year = {2022},
institution = {Research Institute for Symbolic Computation, JKU, Linz},
length = {37}
}

[Banerjee]

Inequalities for the modified Bessel function of first kind of non-negative order

K. Banerjee

Research Institute for Symbolic Computation, JKU, Linz. Technical report no. RISC6608, 2022. [pdf]

[bib]

@techreport{RISC6608,
author = {K. Banerjee},
title = {{Inequalities for the modified Bessel function of first kind of non-negative order}},
language = {english},
number = {RISC6608},
year = {2022},
institution = {Research Institute for Symbolic Computation, JKU, Linz},
length = {28}
}

[Banerjee]

An unified framework to prove multiplicative inequalities for the partition function

K. Banerjee

Research Institute for Symbolic Computation, JKU, Linz. Technical report no. RISC6614, 2022. [pdf]

[bib]

@techreport{RISC6614,
author = {K. Banerjee},
title = {{An unified framework to prove multiplicative inequalities for the partition function}},
language = {english},
number = {RISC6614},
year = {2022},
institution = {Research Institute for Symbolic Computation, JKU, Linz},
length = {24}
}

[Banerjee]

The localization method applied to k-elognated plane partitions and divisibily by 5

K. Banerjee, N. A. Smoot

Research Institute for Symbolic Computation, JKU, Linz. Technical report no. RISC6611, 2022. [pdf]

[bib]

@techreport{RISC6611,
author = {K. Banerjee and N. A. Smoot},
title = {{The localization method applied to k-elognated plane partitions and divisibily by 5}},
language = {english},
number = {RISC6611},
year = {2022},
institution = {Research Institute for Symbolic Computation, JKU, Linz},
length = {40}
}

[Banerjee]

Invariants of the quartic binary form and proofs of Chen's conjectures on partition function inequalities

K. Banerjee

Research Institute for Symbolic Computation, JKU, Linz. Technical report no. RISC6615, 2022. [pdf]

[bib]

@techreport{RISC6615,
author = {K. Banerjee},
title = {{Invariants of the quartic binary form and proofs of Chen's conjectures on partition function inequalities}},
language = {english},
number = {RISC6615},
year = {2022},
institution = {Research Institute for Symbolic Computation, JKU, Linz},
length = {31}
}

[de Freitas]

The Unpolarized and Polarized Single-Mass Three-Loop Heavy Flavor Operator Matrix Elements $A_{gg, Q}$ and $Delta A_{gg, Q}$

J. Ablinger, A. Behring, J. Bluemlein, A. De Freitas, A. Goedicke, A. von Manteuffel, C. Schneider, K. Schoenwald

Journal of High Energy Physics In press, pp. ?-?. 2022. ISSN 1029-8479. arXiv:2211.05462 [hep-ph]. [doi]

[bib]

@article{RISC6632,
author = {J. Ablinger and A. Behring and J. Bluemlein and A. De Freitas and A. Goedicke and A. von Manteuffel and C. Schneider and K. Schoenwald},
title = {{The Unpolarized and Polarized Single-Mass Three-Loop Heavy Flavor Operator Matrix Elements $A_{gg, Q}$ and $Delta A_{gg, Q}$}},
language = {english},
abstract = {We calculate the gluonic massive operator matrix elements in the unpolarized and polarized cases, $A_{gg,Q}(x,mu^2)$ and $Delta A_{gg,Q}(x,mu^2)$, at three--loop order for a single mass. These quantities contribute to the matching of the gluon distribution in the variable flavor number scheme. The polarized operator matrix element is calculated in the Larin scheme. These operator matrix elements contain finite binomial and inverse binomial sums in Mellin $N$--space and iterated integrals over square root--valued alphabets in momentum fraction $x$--space. We derive the necessary analytic relations for the analytic continuation of these quantities from the even or odd Mellin moments into the complex plane, present analytic expressions in momentum fraction $x$--space and derive numerical results. The present results complete the gluon transition matrix elements both of the single-- and double--mass variable flavor number scheme to three--loop order.},
journal = {Journal of High Energy Physics},
volume = {In press},
pages = {?--?},
isbn_issn = { ISSN 1029-8479},
year = {2022},
note = {arXiv:2211.05462 [hep-ph]},
refereed = {yes},
keywords = {Feynman integrals, linear difference equations, linear differential equations, binomial sums, harmonic sums, iterative integrals, computer algebra},
length = {48},
url = {https://doi.org/10.48550/arXiv.2211.05462}
}

[Dominici]

Truncated Hermite polynomials

Diego Dominici and Francisco Marcell{\'a}n

Technical report no. 22-10 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online). August 2022. Licensed under CC BY 4.0 International. [doi] [pdf]

[bib]

@techreport{RISC6531,
author = {Diego Dominici and Francisco Marcell{\'a}n},
title = {{Truncated Hermite polynomials}},
language = {english},
abstract = {We define the family of truncated Hermite polynomials $P_{n}left(x;zright) $, orthogonal with respect to the linear functional[Lleft[ pright] = int_{-z}^{z} pleft( xright) e^{-x^{2}} ,dx. ]The connection of $P_{n}left( x;zright) $ with the Hermite and Rys polynomialsis stated. The semiclassical character of $P_{n}left( x;zright) $ aspolynomials of class $2$ is emphasized.As a consequence, several properties of $P_{n}left( x;zright) $ concerningthe coefficients $gamma_{n}left( zright) $ in the three-term recurrencerelation they satisfy as well as the moments and the Stieltjes function of $L$are given. Ladder operators associated with the linear functional $L$, aholonomic differential equation (in $x)$ for the polynomials $P_{n}left(x;zright) $, and a nonlinear ODE for the functions $gamma_{n}left(zright) $ are deduced. },
number = {22-10},
year = {2022},
month = {August},
keywords = {Orthogonal polynomials, Gaussian distribution},
length = {37},
license = {CC BY 4.0 International},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Altenberger Straße 69, 4040 Linz, Austria},
issn = {2791-4267 (online)}
}

[Dominici]

Comparative asymptotics for discrete semiclassical orthogonal polynomials

Diego Dominici

Technical report no. 22-11 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online). August 2022. Licensed under CC BY 4.0 International. [doi] [pdf]

[bib]

@techreport{RISC6579,
author = {Diego Dominici},
title = {{Comparative asymptotics for discrete semiclassical orthogonal polynomials}},
language = {english},
abstract = {We study the ratio $frac{P_{n}left( x;zright) }{phi_{n}left( xright)}$ asymptotically as $nrightarrowinfty,$ where the polynomials $P_{n}left(x;zright) $ are orthogonal with respect to a discrete linear functional and$phi_{n}left( xright) $ denote the falling factorial polynomials.We give recurrences that allow the computation of high order asymptoticexpansions of $P_{n}left( x;zright) $ and give examples for most discretesemiclassical polynomials of class $sleq2.$We show several plots illustrating the accuracy of our results.},
number = {22-11},
year = {2022},
month = {August},
keywords = {Orthogonal polynomials, asymptotic analysis },
length = {53},
license = {CC BY 4.0 International},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Altenberger Straße 69, 4040 Linz, Austria},
issn = {2791-4267 (online)}
}

[Dominici]

Asymptotic analysis of a family of Sobolev orthogonal polynomials related to the generalized Charlier polynomials

Diego Dominici and Juan José Moreno Balcázar

Technical report no. 22-16 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online). November 2022. Licensed under CC BY 4.0 International. [doi] [pdf]

[bib]

@techreport{RISC6625,
author = {Diego Dominici and Juan José Moreno Balcázar},
title = {{Asymptotic analysis of a family of Sobolev orthogonal polynomials related to the generalized Charlier polynomials}},
language = {english},
abstract = {In this paper we tackle the asymptotic behaviour of a family of orthogonalpolynomials with respect to a nonstandard inner product involving the forwardoperator $Delta$. Concretely, we treat the generalized Charlier weights inthe framework of $Delta$--Sobolev orthogonality. We obtain an asymptoticexpansion for this orthogonal polynomials where the falling factorialpolynomials play an important role.},
number = {22-16},
year = {2022},
month = {November},
keywords = {Sobolev orthogonal polynomials, asymptotic analysis, discrete semiclassical orthogonal polynomials},
length = {18},
license = {CC BY 4.0 International},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Altenberger Straße 69, 4040 Linz, Austria},
issn = {2791-4267 (online)}
}

[Dundua]

Unranked Nominal Unification

Besik Dundua, Temur Kutsia, Mikheil Rukhaia

In: Proceedings of TbiLLC 2019 - 13th International Tbilisi Symposium on Logic, Language, and Computation, Aybüke Özgün and Yulia Zinova (ed.), Proceedings of 13th International Tbilisi Symposium on Logic, Language, and Computation, Lecture Notes in Computer Science 13206, pp. 279-296. 2022. Springer, ISBN 978-3-030-98478-6. [doi] [pdf]

[bib]

@inproceedings{RISC6498,
author = {Besik Dundua and Temur Kutsia and Mikheil Rukhaia},
title = {{Unranked Nominal Unification}},
booktitle = {{Proceedings of TbiLLC 2019 - 13th International Tbilisi Symposium on Logic, Language, and Computation}},
language = {english},
series = {Lecture Notes in Computer Science},
volume = {13206},
pages = {279--296},
publisher = {Springer},
isbn_issn = {ISBN 978-3-030-98478-6},
year = {2022},
editor = {Aybüke Özgün and Yulia Zinova},
refereed = {yes},
length = {17},
conferencename = {13th International Tbilisi Symposium on Logic, Language, and Computation},
url = {https://doi.org/10.1007/978-3-030-98479-3_14}
}

[Falkensteiner]

On Initials and the Fundamental Theorem of Tropical Partial Differential Geometry

S. Falkensteiner, C. Garay-Lopez, M. Haiech, M. P. Noordman, F. Boulier, Z. Toghani

Journal of Symbolic Computation 115, pp. 53-73. 2022. ISSN: 0747-7171. [doi]

[bib]

@article{RISC6335,
author = {S. Falkensteiner and C. Garay-Lopez and M. Haiech and M. P. Noordman and F. Boulier and Z. Toghani},
title = {{On Initials and the Fundamental Theorem of Tropical Partial Differential Geometry}},
language = {english},
journal = {Journal of Symbolic Computation},
volume = {115},
pages = {53--73},
isbn_issn = {ISSN: 0747-7171},
year = {2022},
refereed = {yes},
keywords = {Differential Algebra, Tropical Differential Algebraic Geometry, Power Series Solutions, Newton Polyhedra, Arc Spaces, Tropical Differential Equations, Initial forms of Differential Polynomials},
length = {21},
url = {https://doi.org/10.1016/j.jsc.2022.08.005}
}

[Falkensteiner]

On Formal Power Series Solutions of Algebraic Ordinary Differential Equations

S. Falkensteiner, Yi Zhang, N. Thieu Vo

Mediterranean Journal of Mathematics 19(74), pp. 1-16. March 2022. ISSN 1660-5446. [doi]

[bib]

@article{RISC6490,
author = {S. Falkensteiner and Yi Zhang and N. Thieu Vo},
title = {{On Formal Power Series Solutions of Algebraic Ordinary Differential Equations}},
language = {english},
journal = {Mediterranean Journal of Mathematics},
volume = {19},
number = {74},
pages = {1--16},
isbn_issn = {ISSN 1660-5446},
year = {2022},
month = {March},
refereed = {yes},
keywords = {Formal power series, algebraic differential equation.},
length = {16},
url = {https://doi.org/10.1007/s00009-022-01984-w}
}

[Falkensteiner]

Puiseux Series Solutions with Real or Rational Coefficients of First Order Autonomous AODEs

S. Falkensteiner

In: Proceedings of the 2022 International Symposium on Symbolic and Algebraic Computation, Amir Hashemi (ed.), Proceedings of International Symposium on Symbolic and Algebraic Computation (ISSAC), ISSAC '22 , pp. 63-71. 2022. Association for Computing Machinery, ISBN 9781450386883. [doi]

[bib]

@inproceedings{RISC6585,
author = {S. Falkensteiner},
title = {{Puiseux Series Solutions with Real or Rational Coefficients of First Order Autonomous AODEs}},
booktitle = {{Proceedings of the 2022 International Symposium on Symbolic and Algebraic Computation}},
language = {english},
series = {ISSAC '22},
pages = {63--71},
publisher = {Association for Computing Machinery},
isbn_issn = {ISBN 9781450386883},
year = {2022},
editor = {Amir Hashemi},
refereed = {yes},
length = {9},
conferencename = {International Symposium on Symbolic and Algebraic Computation (ISSAC)},
url = {https://doi.org/10.1145/3476446.3536185}
}

[Grasegger]

Flexible placements of graphs with rotational symmetry

Sean Dewar, Georg Grasegger, Jan Legerský

In: 2nd IMA Conference on Mathematics of Robotics, W. Holderbaum, J.M. Selig (ed.), Springer Proceedings in Advanced Robotics 21, pp. 89-97. 2022. 978-3-030-91351-9. [doi]

[bib]

@inproceedings{RISC6387,
author = {Sean Dewar and Georg Grasegger and Jan Legerský},
title = {{Flexible placements of graphs with rotational symmetry}},
booktitle = {{2nd IMA Conference on Mathematics of Robotics}},
language = {english},
series = {Springer Proceedings in Advanced Robotics},
volume = {21},
pages = {89--97},
isbn_issn = {978-3-030-91351-9},
year = {2022},
editor = {W. Holderbaum and J.M. Selig},
refereed = {yes},
length = {9},
url = {https://doi.org/10.1007/978-3-030-91352-6_9}
}