The Experts below are selected from a list of 288 Experts worldwide ranked by ideXlab platform

Matja Konvalinka - One of the best experts on this subject based on the ideXlab platform.

  • Hook, line and sinker: A bijective proof of the skew shifted hook-Length Formula
    European Journal of Combinatorics, 2020
    Co-Authors: Matja Konvalinka
    Abstract:

    Abstract A few years ago, Naruse presented a beautiful cancellation-free hook-Length Formula for skew shapes, both straight and shifted. The Formula involves a sum over objects called excited diagrams, and the term corresponding to each excited diagram has hook Lengths in the denominator, like the classical hook-Length Formula due to Frame, Robinson and Thrall. Recently, the Formula for skew straight shapes was proved by the author via a simple bumping algorithm. The aim of this paper is to extend this result to skew shifted shapes. Since straight skew shapes are special cases of skew shifted shapes, this is a bijection that proves the whole family of hook-Length Formulas, and is also the simplest known bijective proof for shifted (non-skew) shapes. The complexity of the algorithm is studied, and a weighted generalization of Naruse’s Formula is also presented.

  • a bijective proof of the hook Length Formula for skew shapes
    European Journal of Combinatorics, 2020
    Co-Authors: Matja Konvalinka
    Abstract:

    Abstract Recently, Naruse presented a beautiful cancellation-free hook-Length Formula for skew shapes. The Formula involves a sum over objects called excited diagrams, and the term corresponding to each excited diagram has hook Lengths in the denominator, like the classical hook-Length Formula due to Frame, Robinson and Thrall. In this paper, we present a simple bijection that proves an equivalent recursive version of Naruse’s result, in the same way that the celebrated hook-walk proof due to Greene, Nijenhuis and Wilf gives a bijective (or probabilistic) proof of the hook-Length Formula for ordinary shapes. In particular, we also give a new bijective proof of the classical hook-Length Formula, quite different from the known proofs.

  • Hook, line and sinker: a bijective proof of the skew shifted hook-Length Formula
    arXiv: Combinatorics, 2018
    Co-Authors: Matja Konvalinka
    Abstract:

    A few years ago, Naruse presented a beautiful cancellation-free hook-Length Formula for skew shapes, both straight and shifted. The Formula involves a sum over objects called \emph{excited diagrams}, and the term corresponding to each excited diagram has hook Lengths in the denominator, like the classical hook-Length Formula due to Frame, Robinson and Thrall. Recently, the Formula for skew straight shapes was proved via a simple bumping algorithm. The aim of this paper is to extend this result to skew shifted shapes. Since straight skew shapes are special cases of skew shifted shapes, this is a bijection that proves the whole family of hook-Length Formulas, and is also the simplest known bijective proof for shifted (non-skew) shapes. A weighted generalization of Naruse's Formula is also presented.

  • a bijective proof of the hook Length Formula for skew shapes
    Electronic Notes in Discrete Mathematics, 2017
    Co-Authors: Matja Konvalinka
    Abstract:

    Abstract Recently, Naruse presented a beautiful cancellation-free hook-Length Formula for skew shapes. The Formula involves a sum over objects called excited diagrams, and the term corresponding to each excited diagram has hook Lengths in the denominator, like the classical hook-Length Formula due to Frame, Robinson and Thrall. In this extended abstract, we present a simple bijection that proves an equivalent recursive version of Naruse's result, in the same way that the celebrated hook-walk proof due to Green, Nijenhuis and Wilf gives a bijective (or probabilistic) proof of the hook-Length Formula for ordinary shapes. In particular, we also give a new bijective proof of the classical hook-Length Formula, quite different from the known proofs.

  • a bijective proof of the hook Length Formula for skew shapes
    arXiv: Combinatorics, 2017
    Co-Authors: Matja Konvalinka
    Abstract:

    Recently, Naruse presented a beautiful cancellation-free hook-Length Formula for skew shapes. The Formula involves a sum over objects called excited diagrams, and the term corresponding to each excited diagram has hook Lengths in the denominator, like the classical hook-Length Formula due to Frame, Robinson and Thrall. In this paper, we present a simple bijection that proves an equivalent recursive version of Naruse's result, in the same way that the celebrated hook-walk proof due to Green, Nijenhuis and Wilf gives a bijective (or probabilistic) proof of the hook-Length Formula for ordinary shapes. In particular, we also give a new bijective proof of the classical hook-Length Formula, quite different from the known proofs.

Ghulam Mohammad - One of the best experts on this subject based on the ideXlab platform.

  • On skew cyclic codes over a semi-local ring
    Discrete Mathematics Algorithms and Applications, 2020
    Co-Authors: Mohammad Ashraf, Ghulam Mohammad
    Abstract:

    In the present paper, we study skew cyclic codes over the finite semi-local ring [Formula: see text], where [Formula: see text] and [Formula: see text] is an odd prime. We define a Gray map from [Formula: see text] to [Formula: see text] and investigate the structural properties of skew cyclic codes over [Formula: see text] using decomposition method. It is proved that the Gray image of a skew cyclic code of Length [Formula: see text] over [Formula: see text] is a skew [Formula: see text]-quasi-cyclic code of Length [Formula: see text] over [Formula: see text]. Further, it is shown that the skew cyclic codes over [Formula: see text] are principally generated.

  • Skew cyclic codes over Fq + uFq + vFq
    Asian-European Journal of Mathematics, 2018
    Co-Authors: Mohammad Ashraf, Ghulam Mohammad
    Abstract:

    In this paper, we study skew cyclic codes over the ring [Formula: see text], where [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] is a prime. We define a Gray map from [Formula: see text] to [Formula: see text] and investigate the structural properties of skew cyclic codes over [Formula: see text] using decomposition method. It is shown that the Gray images of skew cyclic codes of Length [Formula: see text] over [Formula: see text] are the skew [Formula: see text]-quasi cyclic codes of Length [Formula: see text] over [Formula: see text]. Finally, the idempotent generators of skew cyclic codes over [Formula: see text] have also been discussed.

Kyung C Chae - One of the best experts on this subject based on the ideXlab platform.

  • a unified queue Length Formula for bmap g 1 queue with generalized vacations
    Stochastic Models, 2002
    Co-Authors: Seok Ho Chang, Tetsuya Takine, Kyung C Chae
    Abstract:

    The main purpose of this article is to demonstrate a unified queue Length Formula for the BMAP/G/1 queue with generalized server vacations. We also present two unified Formulas; one for the distribution of the workload, and the other for the joint distribution of the queue Length and the remaining service time. Some factorizations, which are previously known for M/G/1 queues with vacations and for MAP/G/1 queue with multiple vacations, are now recast in this new framework. Further, based on these Formulas, we provide general recursions for the performance measures of interest.

  • A unified queue Length Formula for BMAP/G/1 queue with generalized vacations
    Stochastic Models, 2002
    Co-Authors: Seok Ho Chang, Tetsuya Takine, Kyung C Chae
    Abstract:

    The main purpose of this article is to demonstrate a unified queue Length Formula for the BMAP/G/1 queue with generalized server vacations. We also present two unified Formulas; one for the distribution of the workload, and the other for the joint distribution of the queue Length and the remaining service time. Some factorizations, which are previously known for M/G/1 queues with vacations and for MAP/G/1 queue with multiple vacations, are now recast in this new framework. Further, based on these Formulas, we provide general recursions for the performance measures of interest.

Mohammad Ashraf - One of the best experts on this subject based on the ideXlab platform.

  • On skew cyclic codes over a semi-local ring
    Discrete Mathematics Algorithms and Applications, 2020
    Co-Authors: Mohammad Ashraf, Ghulam Mohammad
    Abstract:

    In the present paper, we study skew cyclic codes over the finite semi-local ring [Formula: see text], where [Formula: see text] and [Formula: see text] is an odd prime. We define a Gray map from [Formula: see text] to [Formula: see text] and investigate the structural properties of skew cyclic codes over [Formula: see text] using decomposition method. It is proved that the Gray image of a skew cyclic code of Length [Formula: see text] over [Formula: see text] is a skew [Formula: see text]-quasi-cyclic code of Length [Formula: see text] over [Formula: see text]. Further, it is shown that the skew cyclic codes over [Formula: see text] are principally generated.

  • Skew cyclic codes over Fq + uFq + vFq
    Asian-European Journal of Mathematics, 2018
    Co-Authors: Mohammad Ashraf, Ghulam Mohammad
    Abstract:

    In this paper, we study skew cyclic codes over the ring [Formula: see text], where [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] is a prime. We define a Gray map from [Formula: see text] to [Formula: see text] and investigate the structural properties of skew cyclic codes over [Formula: see text] using decomposition method. It is shown that the Gray images of skew cyclic codes of Length [Formula: see text] over [Formula: see text] are the skew [Formula: see text]-quasi cyclic codes of Length [Formula: see text] over [Formula: see text]. Finally, the idempotent generators of skew cyclic codes over [Formula: see text] have also been discussed.

Seok Ho Chang - One of the best experts on this subject based on the ideXlab platform.

  • a unified queue Length Formula for bmap g 1 queue with generalized vacations
    Stochastic Models, 2002
    Co-Authors: Seok Ho Chang, Tetsuya Takine, Kyung C Chae
    Abstract:

    The main purpose of this article is to demonstrate a unified queue Length Formula for the BMAP/G/1 queue with generalized server vacations. We also present two unified Formulas; one for the distribution of the workload, and the other for the joint distribution of the queue Length and the remaining service time. Some factorizations, which are previously known for M/G/1 queues with vacations and for MAP/G/1 queue with multiple vacations, are now recast in this new framework. Further, based on these Formulas, we provide general recursions for the performance measures of interest.

  • A unified queue Length Formula for BMAP/G/1 queue with generalized vacations
    Stochastic Models, 2002
    Co-Authors: Seok Ho Chang, Tetsuya Takine, Kyung C Chae
    Abstract:

    The main purpose of this article is to demonstrate a unified queue Length Formula for the BMAP/G/1 queue with generalized server vacations. We also present two unified Formulas; one for the distribution of the workload, and the other for the joint distribution of the queue Length and the remaining service time. Some factorizations, which are previously known for M/G/1 queues with vacations and for MAP/G/1 queue with multiple vacations, are now recast in this new framework. Further, based on these Formulas, we provide general recursions for the performance measures of interest.