{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T16:59:30Z","timestamp":1776790770038,"version":"3.51.2"},"reference-count":11,"publisher":"American Mathematical Society (AMS)","issue":"267","license":[{"start":{"date-parts":[[2010,1,23]],"date-time":"2010-01-23T00:00:00Z","timestamp":1264204800000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    For an arbitrary matrix\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper A\">\n                        <mml:semantics>\n                          <mml:mi>A<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">A<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    of\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"n times n\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>n<\/mml:mi>\n                            <mml:mo>\n                              \u00d7\n                              \n                            <\/mml:mo>\n                            <mml:mi>n<\/mml:mi>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">n\\times n<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    symbols, consider its submatrices of size\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"k times k\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>k<\/mml:mi>\n                            <mml:mo>\n                              \u00d7\n                              \n                            <\/mml:mo>\n                            <mml:mi>k<\/mml:mi>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">k\\times k<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    , obtained by deleting\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"n minus k\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>n<\/mml:mi>\n                            <mml:mo>\n                              \u2212\n                              \n                            <\/mml:mo>\n                            <mml:mi>k<\/mml:mi>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">n-k<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    rows and\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"n minus k\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>n<\/mml:mi>\n                            <mml:mo>\n                              \u2212\n                              \n                            <\/mml:mo>\n                            <mml:mi>k<\/mml:mi>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">n-k<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    columns. Optionally, the deleted rows and columns can be selected symmetrically or independently. We consider the problem of whether these multisets determine matrix\u00a0\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper A\">\n                        <mml:semantics>\n                          <mml:mi>A<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">A<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    .\n                  <\/p>\n                  <p>\n                    Following the ideas of Krasikov and Roditty in the reconstruction of sequences from subsequences, we replace the multiset by the sum of submatrices. For\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"k greater-than c n Superscript 2 slash 3\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>k<\/mml:mi>\n                            <mml:mo>&gt;<\/mml:mo>\n                            <mml:mi>c<\/mml:mi>\n                            <mml:msup>\n                              <mml:mi>n<\/mml:mi>\n                              <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                <mml:mn>2<\/mml:mn>\n                                <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                  <mml:mo>\/<\/mml:mo>\n                                <\/mml:mrow>\n                                <mml:mn>3<\/mml:mn>\n                              <\/mml:mrow>\n                            <\/mml:msup>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">k&gt;cn^{2\/3}<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    we prove that the matrix\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper A\">\n                        <mml:semantics>\n                          <mml:mi>A<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">A<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    is determined by the sum of the\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"k times k\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>k<\/mml:mi>\n                            <mml:mo>\n                              \u00d7\n                              \n                            <\/mml:mo>\n                            <mml:mi>k<\/mml:mi>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">k\\times k<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    submatrices, both in the symmetric and in the nonsymmetric cases.\n                  <\/p>","DOI":"10.1090\/s0025-5718-09-02210-8","type":"journal-article","created":{"date-parts":[[2009,4,27]],"date-time":"2009-04-27T13:47:33Z","timestamp":1240840053000},"page":"1733-1747","source":"Crossref","is-referenced-by-count":9,"title":["Reconstruction of matrices from submatrices"],"prefix":"10.1090","volume":"78","author":[{"given":"G\u00e9za","family":"K\u00f3s","sequence":"first","affiliation":[]},{"given":"P\u00e9ter","family":"Ligeti","sequence":"additional","affiliation":[]},{"given":"P\u00e9ter","family":"Sziklai","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2009,1,23]]},"reference":[{"issue":"1","key":"1","doi-asserted-by":"publisher","first-page":"22","DOI":"10.1112\/S0024611599011831","article-title":"Littlewood-type problems on [0,1]","volume":"79","author":"Borwein, Peter","year":"1999","journal-title":"Proc. London Math. Soc. (3)","ISSN":"https:\/\/id.crossref.org\/issn\/0024-6115","issn-type":"print"},{"issue":"2","key":"2","doi-asserted-by":"publisher","first-page":"337","DOI":"10.1016\/S0097-3165(03)00103-1","article-title":"Reconstruction from subsequences","volume":"103","author":"Dud\u00edk, Miroslav","year":"2003","journal-title":"J. Combin. Theory Ser. A","ISSN":"https:\/\/id.crossref.org\/issn\/0097-3165","issn-type":"print"},{"issue":"1","key":"3","doi-asserted-by":"publisher","first-page":"102","DOI":"10.1016\/S0196-8858(02)00005-2","article-title":"Inequalities for real-root polynomials and entire functions","volume":"29","author":"Foster, William H.","year":"2002","journal-title":"Adv. in Appl. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0196-8858","issn-type":"print"},{"key":"4","first-page":"56","article-title":"The reconstruction of a word from fragments","author":"Kala\u0161nik, L. I.","year":"1973"},{"key":"5","unstructured":"P. J. Kelly, On isometric transformations. Ph.D. Thesis, University of Wisconsin (1942)."},{"issue":"2","key":"6","doi-asserted-by":"publisher","first-page":"344","DOI":"10.1006\/jcta.1997.2732","article-title":"On a reconstruction problem for sequences","volume":"77","author":"Krasikov, I.","year":"1997","journal-title":"J. Combin. Theory Ser. A","ISSN":"https:\/\/id.crossref.org\/issn\/0097-3165","issn-type":"print"},{"key":"7","doi-asserted-by":"publisher","first-page":"218","DOI":"10.2307\/2689082","article-title":"On reconstruction of matrices","volume":"44","author":"Manvel, Bennet","year":"1971","journal-title":"Math. Mag.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-570X","issn-type":"print"},{"issue":"1","key":"8","doi-asserted-by":"publisher","first-page":"153","DOI":"10.1016\/j.jcta.2004.04.002","article-title":"Excluded permutation matrices and the Stanley-Wilf conjecture","volume":"107","author":"Marcus, Adam","year":"2004","journal-title":"J. Combin. Theory Ser. 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M.","year":"1960"}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.ams.org\/mcom\/2009-78-267\/S0025-5718-09-02210-8\/S0025-5718-09-02210-8.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/mcom\/2009-78-267\/S0025-5718-09-02210-8\/S0025-5718-09-02210-8.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T16:09:34Z","timestamp":1776787774000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/2009-78-267\/S0025-5718-09-02210-8\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,1,23]]},"references-count":11,"journal-issue":{"issue":"267","published-print":{"date-parts":[[2009,7]]}},"alternative-id":["S0025-5718-09-02210-8"],"URL":"https:\/\/doi.org\/10.1090\/s0025-5718-09-02210-8","archive":["CLOCKSS","Portico"],"relation":{},"ISSN":["1088-6842","0025-5718"],"issn-type":[{"value":"1088-6842","type":"electronic"},{"value":"0025-5718","type":"print"}],"subject":[],"published":{"date-parts":[[2009,1,23]]}}}