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Counting minimal reactions with specific conditions in \({\mathbb{R} ^4}\)

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Abstract

We give the sharp lower bound on the number of minimal reactions when no “parallel” species (isomers or multiples) are allowed and all the species are built up from at most four kinds of atoms in Theorem 16. This continues the investigations in Kumar and Pethő (Intern Chem Eng 25:767–769, 1985) through Szalkai and Laflamme (Electr J Comb 5(1), 1998) which results we briefly summarize in the first Section.

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References

  1. Szalkai I., Laflamme C.: Counting Simplexes in \({\mathbb{R}^{n}}\). Hung. J. Ind. Chem. 23, 237–240 (1995) HU ISSN 0133-0276, ref: Chemical Abstract 123, 290982 (1995)

    Google Scholar 

  2. M. Hujter, On the Definition of the n-Dimensional Regular Simplexes Using Inequilities (in Hungarian), Manuscript 6 Mar 2009, see. http://math.bme.hu/~hujter/dekatetr.pdf

  3. Szalkai I.: Handling multicomponent systems in \({\mathbb{R}^{n} }\), I Theoretical results. J. Math. Chem. 25, 31–46 (1999)

    Article  CAS  Google Scholar 

  4. Kumar S., Pethő Á.: Note on a combinatorial problem for the stoichiometry of chemical reactions. Intern. Chem. Eng. 25, 767–769 (1985)

    Google Scholar 

  5. Pethő Á.: The linear relationship between stoichiometry and dimensional analysis. Chem. Eng. Technol. 13, 328–332 (1990)

    Article  Google Scholar 

  6. Fan L.T., Bertók B., Friedler F., Shafie S.: Mechanisms of ammonia-synthesis reaction revisited with the aid of a novel graph-theoretic method. Hung. J. Ind. Chem. 29, 71–80 (2001)

    CAS  Google Scholar 

  7. Fan L.T., Bertók B., Friedler F.: A graph-theoretic method to identify candidate mechanisms. Comput. Chem. 26, 265–292 (2002)

    Article  CAS  Google Scholar 

  8. P. Sellers, Postscript: On the Algebra, Combinatorics & Algorithms for Chemical Reaction Networks. manuscript

  9. P. Sellers, Torsion in Biochemical Reaction Networks. Bulletin of Mathematical Biology (Accepted)

  10. Szalkai I.: Generating minimal reactions in stoichiometry using linear algebra. Hung. J. Ind. Chem. 19, 289–292 (1991)

    CAS  Google Scholar 

  11. Á. Pethő, Lectures on Linear Algebraic Methods in Chemical Engineering Mathematics (stoichiometry). Preprint 1990 (Institut für Technische Chemie, Univ. Hannover, Germany)

  12. Pethő Á.: On a class of solutions of algebraic homogeneous linear equations. Acta Math. Hung. 18, 19–23 (1967)

    Article  Google Scholar 

  13. Appel J., Otarod M., Sellers P.H.: Mechanistic study of chemical reaction systems. Ind. Eng. Chem. Res. 29, 1057–1067 (1990)

    Article  Google Scholar 

  14. I. Szalkai, C. Laflamme, Gy. Dósa, On the maximal and minimal number of bases and simple circuits in matroids and the extremal constructions. Pure Math. Appl. (PUMA) 15, 383–392, HU ISSN 1218–4586 (2006)

    Google Scholar 

  15. I. Szalkai, Private Communication to Cl.Laflamme, 24 Feb 2000

  16. I. Szalkai, C. Laflamme, Counting Simplexes in \({\mathbb{R}^{3}}\). Electr. J. Comb. 5(1), Res. Paper 40, 11 pp (1998). http://www.combinatorics.org. Printed version: J. Combin. 5, 597–607, ref: Current Math. Publ. 1998, No. 16., ZBL 902.05076 (1998)

    Google Scholar 

  17. P. Sellers, Private Communication 7 May 2007

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Correspondence to István Szalkai.

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Szalkai, B., Szalkai, I. Counting minimal reactions with specific conditions in \({\mathbb{R} ^4}\) . J Math Chem 49, 1071–1085 (2011). https://doi.org/10.1007/s10910-010-9798-8

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