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Abstract Detail

Developmental and Structural Section

Mavrodiev, Evgeny V. [1].

Classical invariant theory and plant morphology: conceptual coincidence?

Several authors have indicated the intriguing correspondence between structural chemistry and the theory of algebraic invariants: algebraic binary form of the degree m corresponds to the chemical atom with valence m, and the invariant of a system of binary forms of various degrees is the analogue of a chemical molecule composed of atoms of corresponding valences. The basic method of classical or “symbolic” invariant theory (“Faltungsprozess”) sometimes characterized as an “accurate morphological method”. We propose a simple analogy between invariant theory and the phytonic version of plant morphology: the plant phytomer corresponds to binary form (or bracket “factor of the first kind” (“Faktor erster Art”) itself. The “connection” between two phytomers is described by a “bracket factor of the second kind” (or “Klammerfaktor”), which is a 2 x 2 determinant of two factors of the first kind. In other words, the bracket factor of the second kind is a “convolution” (“Faltung”) or “transvection” (“Uberschiebung”) of two binary forms. For example, the shoot or shoot system built out of a chain of n phytomers can be described as invariant (covariant) of n binary forms which always is a polynominal of the bracket factors of the first and second kind. Irreducible invariants (covariants) containing Hilbert basis of binary form correspond to elementary combinations of phytomers (“articles”). We then postulate that the easiest description of a plant phytomer is the binary form of the third degree so that each plant organ can potentially be described using Hilbert basis of one or several binary forms of the third degree. We can correspond to each combination of phytomers not only an algebraic invariant (covariant) but some natural number which is the “weight” of invariant (covariant). “Weight” is the measure of simplicity of invariant (covariant)

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1 - University of Florida, Department of Botany, Florida Museum of Natural History, P.O. Box 117800, Gainesville, Florida, 32611-7800, USA

Theoretical morphology
classical invariant theory
symbolic method.

Presentation Type: Poster:Posters for Sections
Session: P
Location: Exhibit Hall (Northeast, Southwest & Southeast)/Hilton
Date: Sunday, July 8th, 2007
Time: 8:00 AM
Number: P48016
Abstract ID:1930

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