20.500.12556/RUL-161753 Determinante v kombinatoriki Determinants in combinatorics Veliko matematičnih problemov rešujemo s prevedbo na druge, bolj znane in raziskane probleme. V ta namen pogosto uporabljamo matrike, s katerimi lahko na kompakten način zapišemo lastnosti nekaterih objektov. Ta pristop včasih na bolj ali manj presenetljive načine vodi do determinantnih formul. V tej diplomski nalogi so prikazani nekateri primeri uporabe determinant in determinantnih formul v kombinatoriki. Poudarek je na formulaciji in dokazu Lindström-Gessel-Viennotove leme. Prikazana je tudi njena uporaba, predvsem pri dokazu Binet-Cauchyjevega izreka ter Jacobi-Trudijeve identitete. Cilj je bralcu predstaviti zanimive probleme, v katerih prevedba na teorijo grafov pripelje do elegantne rešitve. Many mathematical problems are solved by translating them into other, better-known and studied problems. For this purpose, matrices are often used to compactly express the properties of certain objects. This approach sometimes, in more or less surprising ways, leads to determinantal formulas. This thesis presents several examples of the use of determinants and determinantal formulas in combinatorics. The focus is on the formulation and proof of the Lindström-Gessel-Viennot lemma. Its application is also demonstrated, particularly in the proof of the Binet-Cauchy theorem and the Jacobi-Trudi identity. The aim is to present the reader with interesting cases where a translation to graph theory leads to an elegant solution. kombinatorika determinante grafi Lindström-Gessel-Viennotova lema simetrični polinomi combinatorics determinants graphs Lindström-Gessel-Viennot lemma symmetric polynomials true false false Slovenski jezik Angleški jezik Diplomsko delo/naloga 2024-09-13 12:25:31 2024-09-13 12:25:35 2024-10-30 09:23:44 0000-00-00 00:00:00 2024 0 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 37248 213385219 Sukovic_Sonja_-_Determinante_v_kombinatoriki.pdf Sukovic_Sonja_-_Determinante_v_kombinatoriki.pdf 1 B408D4A2CA2F304AF443A76EA536A9C6 7fbcd0ca5d8f407ce4a18ff09d2dedd8401ba054239aa611d3b8d9c83f5982ed 732039ea-71ba-11ef-b232-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=190735 Fakulteta za računalništvo in informatiko 0 0 0