17 research outputs found

    Gr\"obner bases of balanced polyominoes

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    We introduce balanced polyominoes and show that their ideal of inner minors is a prime ideal and has a quadratic Gr\"obner basis with respect to any monomial order, and we show that any row or column convex and any tree-like polyomino is simple and balanced

    Many toric ideals generated by quadratic binomials possess no quadratic Gr\"obner bases

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    Let GG be a finite connected simple graph and IGI_{G} the toric ideal of the edge ring K[G]K[G] of GG. In the present paper, we study finite graphs GG with the property that IGI_{G} is generated by quadratic binomials and IGI_{G} possesses no quadratic Gr\"obner basis. First, we give a nontrivial infinite series of finite graphs with the above property. Second, we implement a combinatorial characterization for IGI_{G} to be generated by quadratic binomials and, by means of the computer search, we classify the finite graphs GG with the above property, up to 8 vertices.Comment: 11 pages, 17 figures, Typos corrected, Reference adde

    Toric Rings of Nonsimple Polyominoes

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    Abstract It is known that toric ring of a simple polyomino is ring homomorphic to a edge ring of a weakly chordal bipartite graph. In this paper we identify the attached toric rings of nonsimple polyominoes which are of the form "rectangle minus rectangle". Mathematics Subject Classification: 13C05, 05E4

    Spatially resolved measurement of helium atom emission line spectrum in scrape-off layer of Heliotron J by near-infrared Stokes spectropolarimetry

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    1視線の観測のみで核融合プラズマ中のヘリウム近赤外輝線の発光分布を推定. 京都大学プレスリリース. 2022-09-26.For plasma spectroscopy, Stokes spectropolarimetry is used as a method to spatially invert the viewing-chord-integrated spectrum on the basis of the correspondence between the given magnetic field profile along the viewing chord and the Zeeman effect appearing on the spectrum. Its application to fusion-related toroidal plasmas is, however, limited owing to the low spatial resolution as a result of the difficulty in distinguishing between the Zeeman and Doppler effects. To resolve this issue, we increased the relative magnitude of the Zeeman effect by observing a near-infrared emission line on the basis of the greater wavelength dependence of the Zeeman effect than of the Doppler effect. By utilizing the increased Zeeman effect, we are able to invert the measured spectrum with a high spatial resolution by Monte Carlo particle transport simulation and by reproducing the measured spectra with the semiempirical adjustment of the recycling condition at the first walls. The inversion result revealed that when the momentum exchange collisions of atoms are negligible, the velocity distribution of core-fueling atoms is mainly determined by the initial distribution at the time of recycling. The inversion result was compared with that obtained using a two-point emission model used in previous studies. The latter approximately reflects the parameters of atoms near the emissivity peak

    On the relations of isotonian algebras

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    It is shown that for large classes of posets P and Q, the defining ideal J_{P,Q} of an isotonian algebras is generated by squarefree binomials. Within these classes, those posets are classified for which J_{P,Q} is quadratically generated