On the relations of various conjectures on Latin squares and straightening coefficients
| Autor: | Gian-Carlo Rota, Rosa Huang |
|---|---|
| Jazyk: | angličtina |
| Předmět: |
Discrete mathematics
Rota's basis conjecture Property (philosophy) Bracket algebra Conjecture 010102 general mathematics 0102 computer and information sciences 01 natural sciences Matroid Invariant theory Theoretical Computer Science Combinatorics 010201 computation theory & mathematics Latin square Discrete Mathematics and Combinatorics 0101 mathematics Mathematics Vector space |
| Zdroj: | Discrete Mathematics. (1-3):225-236 |
| ISSN: | 0012-365X |
| DOI: | 10.1016/0012-365X(94)90114-7 |
| Popis: | We discuss the relations among various combinatorial conjectures, to wit: I. A conjecture of J. Dinitz on partial Latin squares, closely related to a conjecture of N. Alon and M. Tarsi on Latin squares. II. A conjecture of the second author on the nonvanishing property of a certain straightening coefficient in the supersymmetric bracket algebra. This conjecture is motivated by the author’s program of extending invariant theory by the use of supersymmetric variables. III. A conjecture of the second author on the exchange property satisfied by sets of bases of a vector space (or more general, for bases of a matroid). IV. A conjecture of J. Kahn which generalizes Dinitz’s conjecture, as well as conjecture III. |
| Databáze: | OpenAIRE |
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