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Multiplicity-Free Key Polynomials
Annals of Combinatorics, 2022 The key polynomials, defined by A. Lascoux-M.-P. Schützenberger, are characters for the Demazure modules of type A. We classify multiplicity-free key polynomials. The proof uses two combinatorial models for key polynomials. The first is due to A. Kohnert. The second is by S. Assaf-D. Searles, in terms of quasi-key polynomials.
Hodges, Reuven, Yong, Alexander
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On multiple q-Laguerre polynomials
Journal of Classical Analysis, 2023 Summary: We study \(q\)-Laguerre multiple orthogonal polynomials. These polynomials are orthogonal with respect to \(q\)-analogues of Laguerre weight functions. We focus our attention on their structural properties. Raising and lowering operators as well as Rodrigues-type formulas are obtained and their explicit representations are given.
Sadjang, P. Njionou +2 more
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IEEE Access, 2020 In a distributed computing environment, there may exist slow processing workers, which are known as “stragglers”, and they can slow down the whole computing process.
Sangwoo Hong, Heecheol Yang, Jungwoo Lee
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Racing BIKE: Improved Polynomial Multiplication and Inversion in Hardware
Transactions on Cryptographic Hardware and Embedded Systems, 2021 BIKE is a Key Encapsulation Mechanism selected as an alternate candidate in NIST’s PQC standardization process, in which performance plays a significant role in the third round.
Jan Richter-Brockmann +3 more
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Area-Efficient Polynomial Multiplication Hardware Implementation for Lattice-based Cryptography [PDF]
Jisuanji gongchengLattice-based post-quantum cryptography algorithms demonstrate significant potential in public-key cryptography. A key performance bottleneck in hardware implementation is the computational complexity of polynomial multiplication. To address the problems
XIE Jiaxing, PU Jinwei, FANG Weitian, ZHENG Xin, XIONG Xiaoming
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Global existence and blow up of solution for semi-linear hyperbolic equation with the product of logarithmic and power-type nonlinearity [PDF]
Opuscula Mathematica, 2020 In this paper we consider the semilinear wave equation with the multiplication of logarithmic and polynomial nonlinearities. We establish the global existence and finite time blow up of solutions at three different energy levels (\(E(0)\lt d\), \(E(0)=d\)
Wei Lian, Md Salik Ahmed, Runzhang Xu
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Efficient Homomorphic Encryption Accelerator With Integrated PRNG Using Low-Cost FPGA
IEEE Access, 2022 With recent development in internet speed and reliability, cloud computing has become a more reliable solution for the user. In many cases where data privacy is critical, fully homomorphic encryption (FHE) can be a security solution for securing cloud ...
Infall Syafalni +4 more
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A lower bound for the multiplication of polynomials modulo a polynomial [PDF]
Information Processing Letters, 1992 In 1983 \textit{A. Lempel}, \textit{G. Seroussi} and \textit{S. Winograd} [Theor. Comput. Sci. 22, 285-296 (1983; Zbl 0498.68027)] proved the lower bound \((2+1/(q-1))n-o(n)\) for the multiplicative complexity of the multiplication of two polynomials of degree \(n-1\) modulo an irreducible polynomial \(p\) of degree \(n\) over a finite field \(F\) with
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On Littlewood and Newman polynomial multiples of Borwein polynomials
Mathematics of Computation, 2017 Polynomials with coefficients in the sets \(\{-1,1\}\), \(\{0,1\}\) and \(\{-1,0,1\}\) are called Littlewood-Newman-Borwein polynomials, respectively. In [Math. Comput. 78, No. 265, 327--344 (2009; Zbl 1208.11123)], the reviewer and the second author investigated various divisibility relations between these three sets of polynomials.
Paulius Drungilas +2 more
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Parallel Integer Polynomial Multiplication [PDF]
2016 18th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC), 2016 We propose a new algorithm for multiplying dense polynomials with integer coefficients in a parallel fashion, targeting multi-core processor architectures. Complexity estimates and experimental comparisons demonstrate the advantages of this new approach.
Chen, Changbo +5 more
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