On some primary and secondary structures in combinatorics
نویسنده
چکیده
A possible upgrade of a curriculum in undergraduate course in combinatorics is presented by giving more bijective proofs in the standard (or primary) combinatorics and by adding some topics on more refined (or secondary) combinatorics, including Dyck and Motzkin paths, Catalan, Narayana and Motzkin numbers and secondary structures coming from biology. Some log–convexity properties and asymptotics of these numbers are also presented.
منابع مشابه
Comparative Phylogenetic Perspectives on the Evolutionary Relationships in the Brine Shrimp Artemia Leach, 1819 (Crustacea: Anostraca) Based on Secondary Structure of ITS1 Gene
This is the first study on phylogenetic relationships in the genus Artemia Leach, 1819 using the pattern and sequence of secondary structures of internal transcribed spacer 1 (ITS1). Significant intraspecific variation in the secondary structure of ITS1 rRNA was found in Artemia tibetiana. In the phylogenetic tree based on joined primary and secondary structure sequences, Artemia urmiana and pa...
متن کاملPhylogenetic Analysis of Beta-Glucanase Producing Actinomycetes Strain TBG-CH22 - A Comparison of Conventional and Molecular Morphometric Approach
Actinomycetes are inexhaustible producers of commercially valuable metabolites, are continually screened for beneficial compounds. The taxonomic and phylogenetic study of novel actinomycetes strains are mostly based on conventional methods and primary DNA structure of 16s rRNA. Although 16s rRNA sequence is well accepted in phylogeny studies, its secondary structures have not been widely used. ...
متن کاملPhylogenetic Analysis of Beta-Glucanase Producing Actinomycetes Strain TBG-CH22 - A Comparison of Conventional and Molecular Morphometric Approach
Actinomycetes are inexhaustible producers of commercially valuable metabolites, are continually screened for beneficial compounds. The taxonomic and phylogenetic study of novel actinomycetes strains are mostly based on conventional methods and primary DNA structure of 16s rRNA. Although 16s rRNA sequence is well accepted in phylogeny studies, its secondary structures have not been widely used. ...
متن کاملGeometric and Electronic Structures of Vanadium Sub-nano Clusters, Vn (n = 2-5), and their Adsorption Complexes with CO and O2 Ligands: A DFT-NBO Study
In this study, electronic structures of ground state of pure vanadium sub-nano clusters, Vn (n=2-5), and their interactions with small ligands for example CO and triplet O2 molecules are investigated by using density functional theory (DFT) calibration at the mPWPW91/QZVP level of theory. The favorable orientations of these ligands in interaction with pure vanadium sub-nano clusters were determ...
متن کاملRelation Between RNA Sequences, Structures, and Shapes via Variation Networks
Background: RNA plays key role in many aspects of biological processes and its tertiary structure is critical for its biological function. RNA secondary structure represents various significant portions of RNA tertiary structure. Since the biological function of RNA is concluded indirectly from its primary structure, it would be important to analyze the relations between the RNA sequences and t...
متن کامل