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Stability of characters and filters for weighted semilattices

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Stability of characters and filters for weighted semilattices. / Choi, Yemon; Ghandehari, Mahya; Pham, Hung Le.
In: Semigroup Forum, Vol. 102, No. 1, 11.02.2021, p. 86-103.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Choi, Y, Ghandehari, M & Pham, HL 2021, 'Stability of characters and filters for weighted semilattices', Semigroup Forum, vol. 102, no. 1, pp. 86-103. https://doi.org/10.1007/s00233-020-10147-w

APA

Choi, Y., Ghandehari, M., & Pham, H. L. (2021). Stability of characters and filters for weighted semilattices. Semigroup Forum, 102(1), 86-103. https://doi.org/10.1007/s00233-020-10147-w

Vancouver

Choi Y, Ghandehari M, Pham HL. Stability of characters and filters for weighted semilattices. Semigroup Forum. 2021 Feb 11;102(1):86-103. Epub 2020 Dec 24. doi: 10.1007/s00233-020-10147-w

Author

Choi, Yemon ; Ghandehari, Mahya ; Pham, Hung Le. / Stability of characters and filters for weighted semilattices. In: Semigroup Forum. 2021 ; Vol. 102, No. 1. pp. 86-103.

Bibtex

@article{54dd293cfcf94285883aeac44771b4ce,
title = "Stability of characters and filters for weighted semilattices",
abstract = "We continue the study of the AMNM property for weighted semilattices that was initiated in [Y. Choi, J. Austral. Math. Soc. 95 (2013), no. 1, 36-67; arXiv 1203.6691 ] . We reformulate this in terms of stability of filters with respect to a given weight function, and then provide a combinatorial condition which is necessary and sufficient for this {"}filter stability{"} property to hold. Examples are given to show that this new condition allows for easier and unified proofs of some results in [Choi, ibid. ] , and furthermore allows us to verify the AMNM property in situations not covered by the results of that paper. As a final application, we show that for a large class of semilattices, arising naturally as union-closed set systems, one can always construct weights for which the AMNM property fails.",
author = "Yemon Choi and Mahya Ghandehari and Pham, {Hung Le}",
year = "2021",
month = feb,
day = "11",
doi = "10.1007/s00233-020-10147-w",
language = "English",
volume = "102",
pages = "86--103",
journal = "Semigroup Forum",
issn = "0037-1912",
publisher = "Springer New York",
number = "1",

}

RIS

TY - JOUR

T1 - Stability of characters and filters for weighted semilattices

AU - Choi, Yemon

AU - Ghandehari, Mahya

AU - Pham, Hung Le

PY - 2021/2/11

Y1 - 2021/2/11

N2 - We continue the study of the AMNM property for weighted semilattices that was initiated in [Y. Choi, J. Austral. Math. Soc. 95 (2013), no. 1, 36-67; arXiv 1203.6691 ] . We reformulate this in terms of stability of filters with respect to a given weight function, and then provide a combinatorial condition which is necessary and sufficient for this "filter stability" property to hold. Examples are given to show that this new condition allows for easier and unified proofs of some results in [Choi, ibid. ] , and furthermore allows us to verify the AMNM property in situations not covered by the results of that paper. As a final application, we show that for a large class of semilattices, arising naturally as union-closed set systems, one can always construct weights for which the AMNM property fails.

AB - We continue the study of the AMNM property for weighted semilattices that was initiated in [Y. Choi, J. Austral. Math. Soc. 95 (2013), no. 1, 36-67; arXiv 1203.6691 ] . We reformulate this in terms of stability of filters with respect to a given weight function, and then provide a combinatorial condition which is necessary and sufficient for this "filter stability" property to hold. Examples are given to show that this new condition allows for easier and unified proofs of some results in [Choi, ibid. ] , and furthermore allows us to verify the AMNM property in situations not covered by the results of that paper. As a final application, we show that for a large class of semilattices, arising naturally as union-closed set systems, one can always construct weights for which the AMNM property fails.

U2 - 10.1007/s00233-020-10147-w

DO - 10.1007/s00233-020-10147-w

M3 - Journal article

VL - 102

SP - 86

EP - 103

JO - Semigroup Forum

JF - Semigroup Forum

SN - 0037-1912

IS - 1

ER -