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Topology"],"published-print":{"date-parts":[[2024,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We implement an algorithm <jats:italic>RSHT (random simple-homotopy)<\/jats:italic> to study the simple-homotopy types of simplicial complexes, with a particular focus on contractible spaces and on finding substructures in higher-dimensional complexes. The algorithm combines elementary simplicial collapses with <jats:italic>pure elementary expansions<\/jats:italic>. For triangulated <jats:italic>d<\/jats:italic>-manifolds with <jats:inline-formula><jats:alternatives><jats:tex-math>$$d\\le 6$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>d<\/mml:mi>\n                    <mml:mo>\u2264<\/mml:mo>\n                    <mml:mn>6<\/mml:mn>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>, we show that RSHT reduces to (random) bistellar flips. Among the many examples on which we test RSHT, we describe an explicit 15-vertex triangulation of the Abalone, and more generally, <jats:inline-formula><jats:alternatives><jats:tex-math>$$(14k+1)$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mo>(<\/mml:mo>\n                    <mml:mn>14<\/mml:mn>\n                    <mml:mi>k<\/mml:mi>\n                    <mml:mo>+<\/mml:mo>\n                    <mml:mn>1<\/mml:mn>\n                    <mml:mo>)<\/mml:mo>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-vertex triangulations of a new series of Bing\u2019s houses with <jats:italic>k<\/jats:italic> rooms, <jats:inline-formula><jats:alternatives><jats:tex-math>$$k\\ge 3$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>k<\/mml:mi>\n                    <mml:mo>\u2265<\/mml:mo>\n                    <mml:mn>3<\/mml:mn>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>, which all can be deformed to a point using only six pure elementary expansions.\n<\/jats:p>","DOI":"10.1007\/s41468-023-00139-4","type":"journal-article","created":{"date-parts":[[2023,10,28]],"date-time":"2023-10-28T15:01:41Z","timestamp":1698505301000},"page":"531-555","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Random simple-homotopy theory"],"prefix":"10.1007","volume":"8","author":[{"given":"Bruno","family":"Benedetti","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Crystal","family":"Lai","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Davide","family":"Lofano","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Frank H.","family":"Lutz","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,10,28]]},"reference":[{"issue":"4","key":"139_CR1","doi-asserted-by":"publisher","first-page":"824","DOI":"10.1007\/s00454-017-9860-4","volume":"57","author":"KA Adiprasito","year":"2017","unstructured":"Adiprasito, K.A., Benedetti, B., Lutz, F.H.: Extremal examples of collapsible complexes and random discrete Morse theory. 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