The Laurent Coefficients of the Hilbert Series of a Gorenstein Algebra

References

• [Abramowitz and Stegun 64] M. Abramowitz and I. A. Stegun, (1964). Handbook of mathematical functions with formulas, graphs, and mathematical tables, Vol. 55 of National Bureau of Standards Applied Mathematics Series. For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C.
   Google Scholar
• [Benson 93] D. J. Benson. Polynomial Invariants of Finite Groups, Vol. 190 of London Mathematical Society Lecture Note Series. Cambridge: Cambridge University Press, 1993.
   Google Scholar
• [Bruns and Herzog 93] W. Bruns and J. Herzog. Cohen-Macaulay rings, Vol. 39 of Cambridge Studies in Advanced Mathematics. Cambridge: Cambridge University Press, 1993.
   Google Scholar
• [Carlitz 70] L. Carlitz. “Note on Certain Triangular Arrays.” SIAM J. Math. Anal. 1 (1970), 328–332.
   Google Scholar
• [Cayres Pinto et al. 18] P. D. C. Cayres Pinto, H.-C. Herbig, D. Herden, and C. Seaton. “The Hilbert Series of SL2-Invariants.” Preprint, arXiv:1710.02606v3 [math.RA], 2018.
   Google Scholar
• [Cowie et al. 19] L. E. Cowie, H.-C. Herbig, D. Herden and C. Seaton. “The Hilbert Series and a-Invariant of Circle Invariants.” J. Pure Appl. Algebra. 223 (2019), 395–421.
   Google Scholar
• [Derksen and Kemper 02] H. Derksen and G. Kemper. Computational invariant theory. Invariant Theory and Algebraic Transformation Groups, I. Encyclopaedia of Mathematical Sciences, 130. Berlin: Springer-Verlag, 2002.
   Google Scholar
• [Feinberg 67] M. Feinberg. “A Lucas Triangle.” Fibonacci Quart. 5 (1967), 486–490.
   Google Scholar
• [Gessel 03] I. M. Gessel. “Applications of the Classical Umbral Calculus.” Algebra Universalis. 49:4 (2003), 397–434. Dedicated to the memory of Gian-Carlo Rota.
   Web of Science ®Google Scholar
• [Gould 69] H. W. Gould. “Power Sum Identities for Arbitrary Symmetric Arrays.” SIAM J. Appl. Math. 17 (1969), 307–316.
   Web of Science ®Google Scholar
• [Herbig et al. 15] H.-C. Herbig, D. Herden, and C. Seaton. “ On Compositions with x2/(1−x).” Proc. Amer. Math. Soc. 143 (2015), 4583–4596.
   Web of Science ®Google Scholar
• [Herbig and Seaton 14] H.-C. Herbig and C. Seaton. “The Hilbert Series of a Linear Symplectic Circle Quotient.” Exp. Math. 23:1 (2014), 46–65.
   Web of Science ®Google Scholar
• [Kempf 79] G. Kempf. “The Hochster-Roberts Theorem of Invariant Theory.” Michigan Math. J., 26:1 (1979), 19–32.
   Web of Science ®Google Scholar
• [Moll 12] V. H. Moll. Numbers and Functions, Vol. 65 of Student Mathematical Library. Providence, RI: American Mathematical Society, 2012. From a classical-experimental mathematician’s point of view.
   Google Scholar
• [Mordell 73] L. J. Mordell. “The Sign of the Bernoulli Numbers.” Amer. Math. Monthly 80 (1973), 547–548.
   Web of Science ®Google Scholar
• [Popov and Vinberg 94] V. L. Popov and È. B. Vinberg. “Invariant Theory”. In Algebraic geometry. IV, Vol. 55 of Encyclopaedia of Mathematical Sciences, pages vi +284. Springer-Verlag, Berlin. Linear algebraic groups. Invariant theory, A translation of it Algebraic geometry. 4 (Russian), Akad. Nauk SSSR Vsesoyuz. Inst. Nauchn. i Tekhn. Inform., Moscow, 1989, Translation edited by A. N. Parshin and I. R. Shafarevich.
   Google Scholar
• [Robbins 05] N. Robbins. “The Lucas Triangle Revisited.” Fibonacci Quart. 43:2 (2005),142–148.
   Web of Science ®Google Scholar
• [Sloane 14] N. J. A. Sloane. “Online Encyclopaedia of Integer Sequences.” Available online (https://oeis.org), 2014.
   Google Scholar
• [Stanley 78] R. P. Stanley. “Hilbert Functions of Graded Algebras.” Advances in Math. 28:1 (1978), 57–83.
   Google Scholar
• [Sturmfels 93] B. Sturmfels. Algorithms in Invariant Theory. Texts and Monographs in Symbolic Computation. Vienna: Springer-Verlag, 1993.
   Google Scholar
• [Villarreal 15] R. H. Villarreal. Monomial Algebras. Monographs and Research Notes in Mathematics. Second edition. Boca Raton, FL: CRC Press, 2015.
   Google Scholar
• [Watanabe 74a] K. Watanabe. “Certain Invariant Subrings are Gorenstein. I.” Osaka J. Math. 11 (1974a), 1–8.
   Google Scholar
• [Watanabe 74b] K. Watanabe. “Certain Invariant Subrings are Gorenstein. II.” Osaka J. Math. 11 (1974b), 379–388.
   Google Scholar
• [Wolfram Research 14] Wolfram Research. “Mathematica Edition,” Release 10.0. Available at http://www.wolfram.com/mathematica/.
   Google Scholar