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Signed counting of partition matrices.

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Title: Signed counting of partition matrices.
Authors: Chern, Shane1 (AUTHOR) chenxiaohang92@gmail.com, Fu, Shishuo1,2,3 (AUTHOR) fsshuo@cqu.edu.cn
Source: Journal of Combinatorial Theory - Series A. Oct2026, Vol. 223, pN.PAG-N.PAG. 1p.
Subjects: Matrices (Mathematics), Combinatorial enumeration problems
Abstract: We prove that the signed counting (with respect to the parity of the "inv" statistic) of partition matrices equals the cardinality of a subclass of inversion sequences. In the course of establishing this result, we introduce an interesting class of partition matrices called improper partition matrices. We further show that a subset of improper partition matrices is counted by the Motzkin numbers. Such an enumeration is established both analytically and bijectively, building upon a combinatorial mechanism involving weighted Motzkin paths. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Combinatorial Theory - Series A is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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Header DbId: egs
DbLabel: Engineering Source
An: 194372131
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
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  Data: Signed counting of partition matrices.
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  Data: <searchLink fieldCode="AR" term="%22Chern%2C+Shane%22">Chern, Shane</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> chenxiaohang92@gmail.com</i><br /><searchLink fieldCode="AR" term="%22Fu%2C+Shishuo%22">Fu, Shishuo</searchLink><relatesTo>1,2,3</relatesTo> (AUTHOR)<i> fsshuo@cqu.edu.cn</i>
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+Combinatorial+Theory+-+Series+A%22">Journal of Combinatorial Theory - Series A</searchLink>. Oct2026, Vol. 223, pN.PAG-N.PAG. 1p.
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  Data: We prove that the signed counting (with respect to the parity of the "inv" statistic) of partition matrices equals the cardinality of a subclass of inversion sequences. In the course of establishing this result, we introduce an interesting class of partition matrices called improper partition matrices. We further show that a subset of improper partition matrices is counted by the Motzkin numbers. Such an enumeration is established both analytically and bijectively, building upon a combinatorial mechanism involving weighted Motzkin paths. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Journal of Combinatorial Theory - Series A is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1016/j.jcta.2026.106213
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 1
        StartPage: N.PAG
    Subjects:
      – SubjectFull: Matrices (Mathematics)
        Type: general
      – SubjectFull: Combinatorial enumeration problems
        Type: general
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      – TitleFull: Signed counting of partition matrices.
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          Name:
            NameFull: Chern, Shane
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          Name:
            NameFull: Fu, Shishuo
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          Dates:
            – D: 01
              M: 10
              Text: Oct2026
              Type: published
              Y: 2026
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            – Type: issn-print
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              Value: 223
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            – TitleFull: Journal of Combinatorial Theory - Series A
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