{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T05:45:42Z","timestamp":1776836742971,"version":"3.51.2"},"reference-count":20,"publisher":"American Mathematical Society (AMS)","issue":"341","license":[{"start":{"date-parts":[[2024,1,23]],"date-time":"2024-01-23T00:00:00Z","timestamp":1705968000000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"funder":[{"DOI":"10.13039\/501100004442","name":"Narodowym Centrum Nauki","doi-asserted-by":"publisher","award":["2020\/39\/B\/HS1\/00216"],"award-info":[{"award-number":["2020\/39\/B\/HS1\/00216"]}],"id":[{"id":"10.13039\/501100004442","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004442","name":"Narodowym Centrum Nauki","doi-asserted-by":"publisher","award":["Oberwolfach Research Fellows Program"],"award-info":[{"award-number":["Oberwolfach Research Fellows Program"]}],"id":[{"id":"10.13039\/501100004442","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100014398","name":"Mathematisches Forschungsinstitut Oberwolfach","doi-asserted-by":"publisher","award":["2020\/39\/B\/HS1\/00216"],"award-info":[{"award-number":["2020\/39\/B\/HS1\/00216"]}],"id":[{"id":"10.13039\/501100014398","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100014398","name":"Mathematisches Forschungsinstitut Oberwolfach","doi-asserted-by":"publisher","award":["Oberwolfach Research Fellows Program"],"award-info":[{"award-number":["Oberwolfach Research Fellows Program"]}],"id":[{"id":"10.13039\/501100014398","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    We use Constraint Satisfaction Methods to construct and enumerate finite\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper L\">\n                        <mml:semantics>\n                          <mml:mi>L<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">L<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    -algebras up to isomorphism. These objects were recently introduced by Rump and appear in Garside theory, algebraic logic, and the study of the combinatorial Yang\u2013Baxter equation. There are 377,322,225 isomorphism classes of\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper L\">\n                        <mml:semantics>\n                          <mml:mi>L<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">L<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    -algebras of size eight. The database constructed suggests the existence of bijections between certain classes of\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper L\">\n                        <mml:semantics>\n                          <mml:mi>L<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">L<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    -algebras and well-known combinatorial objects. We prove that Bell numbers enumerate isomorphism classes of finite linear\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper L\">\n                        <mml:semantics>\n                          <mml:mi>L<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">L<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    -algebras. We also prove that finite regular\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper L\">\n                        <mml:semantics>\n                          <mml:mi>L<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">L<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    -algebras are in bijective correspondence with infinite-dimensional Young diagrams.\n                  <\/p>","DOI":"10.1090\/mcom\/3814","type":"journal-article","created":{"date-parts":[[2023,1,23]],"date-time":"2023-01-23T15:17:19Z","timestamp":1674487039000},"page":"1363-1381","source":"Crossref","is-referenced-by-count":0,"title":["On the enumeration of finite \ud835\udc3f-algebras"],"prefix":"10.1090","volume":"92","author":[{"given":"C.","family":"Dietzel","sequence":"first","affiliation":[]},{"given":"P.","family":"Mench\u00f3n","sequence":"additional","affiliation":[]},{"given":"L.","family":"Vendramin","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2023,1,23]]},"reference":[{"issue":"335","key":"1","doi-asserted-by":"publisher","first-page":"1469","DOI":"10.1090\/mcom\/3696","article-title":"Enumeration of set-theoretic solutions to the Yang-Baxter equation","volume":"91","author":"Akg\u00fcn, \u00d6.","year":"2022","journal-title":"Math. 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Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0001-8708","issn-type":"print"},{"key":"4","series-title":"EMS Tracts in Mathematics","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.4171\/139","volume-title":"Foundations of Garside theory","volume":"22","author":"Dehornoy, Patrick","year":"2015","ISBN":"https:\/\/id.crossref.org\/isbn\/9783037191392"},{"key":"5","series-title":"Collection de Logique Math\\'{e}matique, S\\'{e}r. A, Fasc. XXI","volume-title":"Sur les alg\\`ebres de Hilbert","author":"Diego, Antonio","year":"1966"},{"key":"6","unstructured":"The GAP Group, GAP \u2013 groups, algorithms, and programming, version 4.11.1, 2021."},{"key":"7","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1305\/ndjfl\/1093891789","article-title":"Implication connectives in orthomodular lattices","volume":"16","author":"Herman, L.","year":"1975","journal-title":"Notre Dame J. 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