Enumeration of pattern avoiding compositions of numbers Abstract The aim of this work was to find some new results for 3-regular compositions, i.e., for those compositions which avoid the set of patterns {121, 212, 11}. Those compositions can be regarded as a generalization of Carlitz composition. Based on the generating function of compositions avoiding the set of patterns {121, 11} and {212, 11} we derive an upper bound for the coefficients of the power series of the generating function of 3-regular compositions. Using the theory of finite automata we derive its lower bound. We develop this result further by defining 3-block compositions. For the generating function of 3-regular compositions we prove a recursive ralation. Besides that we also compute the generating function of compositions avoiding the set of patterns {312, 321} whose parts are in the set [d]. In the last section we prove that the generating function of Carlitz compositions is transcendental.
| Identifer | oai:union.ndltd.org:nusl.cz/oai:invenio.nusl.cz:330716 |
| Date | January 2013 |
| Creators | Dodova, Borjana |
| Contributors | Klazar, Martin, Jelínek, Vít |
| Source Sets | Czech ETDs |
| Language | Czech |
| Detected Language | English |
| Type | info:eu-repo/semantics/masterThesis |
| Rights | info:eu-repo/semantics/restrictedAccess |
Page generated in 0.0018 seconds