[seqfan] enumeration of siphons in chemical reaction networks

Jonathan Post jvospost3 at gmail.com
Thu Jan 7 22:22:29 CET 2010

26, 2300, 42504, 245157, 497420, 352716, 77520, 3876, 18

offset 24, 1

"The number of minimal siphons satisfies the recursion N(s) = N(s - 2)
+ N(s - 3), where N(2) = 2, N(3) = 2, and N(4) = 3. For s = 50 species
obtain N(50) = 1,221,537."

 From table on pp.15-16

Replacements for Wed, 6 Jan 10

    Title: Siphons in chemical reaction networks
    Authors: Anne Shiu, Bernd Sturmfels
    Subjects: Commutative Algebra (math.AC); Molecular Networks (q-bio.MN)

Siphons in a chemical reaction system are subsets of the species that
have the potential of being absent in a steady state. We present a
characterization of minimal siphons in terms of primary decomposition
of binomial ideals, we explore the underlying geometry, and we
demonstrate the effective computation of siphons using computer
algebra software. This leads to a new method for determining whether
given initial concentrations allow for various boundary steady states.

Or is this arbitrary (s = 50) and better presented as an array?

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