{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,27]],"date-time":"2025-06-27T22:40:02Z","timestamp":1751064002128,"version":"3.41.0"},"reference-count":0,"publisher":"Combinatorial Press","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Ars Comb."],"published-print":{"date-parts":[[2025,6,28]]},"abstract":"<jats:p>&lt;p&gt;We apply the splitting operation defined on binary matroids (Raghunathan et al., 1998) to &lt;span class=\"math inline\"&gt;\\(p\\)&lt;\/span&gt;- matroids, where &lt;span class=\"math inline\"&gt;\\(p\\)&lt;\/span&gt;-matroids refer to matroids representable over &lt;span class=\"math inline\"&gt;\\(GF(p).\\)&lt;\/span&gt; We also characterize circuits, bases, and independent sets of the resulting matroid. Sufficient conditions to yield Eulerian &lt;span class=\"math inline\"&gt;\\(p\\)&lt;\/span&gt;-matroids from Eulerian and non-Eulerian &lt;span class=\"math inline\"&gt;\\(p\\)&lt;\/span&gt;-matroids by applying the splitting operation are obtained. A class of connected &lt;span class=\"math inline\"&gt;\\(p\\)&lt;\/span&gt;-matroids that gives connected &lt;span class=\"math inline\"&gt;\\(p\\)&lt;\/span&gt;-matroids under the splitting operation is characterized. In Application, we characterize a class of paving &lt;span class=\"math inline\"&gt;\\(p\\)&lt;\/span&gt;-matroids, which produces paving matroids after the splitting operation.&lt;\/p&gt;<\/jats:p>","DOI":"10.61091\/ars163-02","type":"journal-article","created":{"date-parts":[[2025,6,27]],"date-time":"2025-06-27T22:01:43Z","timestamp":1751061703000},"page":"13-27","source":"Crossref","is-referenced-by-count":0,"title":["On the circuits of splitting matroids representable over  GF(p)"],"prefix":"10.61091","volume":"163","author":[{"name":"Department of Mathematics and Statistics, Dr. Vishwanath Karad MIT-World Peace University, Pune-38, India","sequence":"first","affiliation":[]},{"given":"Prashant","family":"Malavadkar","sequence":"first","affiliation":[]},{"given":"Uday","family":"Jagadale","sequence":"additional","affiliation":[]},{"name":"Department of Mathematics and Statistics, Dr. Vishwanath Karad MIT-World Peace University, Pune-38, India","sequence":"additional","affiliation":[]},{"given":"Sachin","family":"Gunjal","sequence":"additional","affiliation":[]},{"name":"Department of Mathematics and Statistics, Dr. Vishwanath Karad MIT-World Peace University, Pune-38, India","sequence":"additional","affiliation":[]}],"member":"39747","published-online":{"date-parts":[[2025,6,28]]},"container-title":["Ars Combinatoria"],"original-title":[],"deposited":{"date-parts":[[2025,6,27]],"date-time":"2025-06-27T22:01:45Z","timestamp":1751061705000},"score":1,"resource":{"primary":{"URL":"https:\/\/combinatorialpress.com\/ars-articles\/volume-163\/on-the-circuits-of-splitting-matroids-representable-over-gfp\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,6,28]]},"references-count":0,"URL":"https:\/\/doi.org\/10.61091\/ars163-02","relation":{},"ISSN":["0381-7032","2817-5204"],"issn-type":[{"value":"0381-7032","type":"print"},{"value":"2817-5204","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,6,28]]}}}