scholarly journals Equivariant Hilbert series in non-noetherian polynomial rings

2017 ◽  
Vol 486 ◽  
pp. 204-245 ◽  
Author(s):  
Uwe Nagel ◽  
Tim Römer
Keyword(s):  
Hilbert Series ◽  
Polynomial Rings

scholarly journals Hilbert series of symmetric ideals in infinite polynomial rings via formal languages

2017 ◽  
Vol 485 ◽  
pp. 353-362 ◽  
Author(s):  
Robert Krone ◽  
Anton Leykin ◽  
Andrew Snowden
Keyword(s):  
Hilbert Series ◽  
Formal Languages ◽  
Polynomial Rings

scholarly journals Which series are Hilbert series of graded modules over standard multigraded polynomial rings?

2019 ◽  
Vol 293 (1) ◽  
pp. 129-146
Author(s):  
Lukas Katthän ◽  
Julio José Moyano‐Fernández ◽  
Jan Uliczka
Keyword(s):  
Hilbert Series ◽  
Polynomial Rings ◽  
Graded Modules

scholarly journals Hilbert series of modules over positively graded polynomial rings

2016 ◽  
Vol 459 ◽  
pp. 437-445 ◽  
Author(s):  
Lukas Katthän ◽  
Julio José Moyano-Fernández ◽  
Jan Uliczka
Keyword(s):  
Hilbert Series ◽  
Polynomial Rings

scholarly journals Intersection algebras for principal monomial ideals in polynomial rings

2015 ◽  
Vol 14 (07) ◽  
pp. 1550108 ◽  
Author(s):  
Florian Enescu ◽  
Sara Malec
Keyword(s):  
Polynomial Ring ◽  
Hilbert Series ◽  
Linear Equations ◽  
Monomial Ideals ◽  
Polynomial Rings ◽  
Integer Coefficients ◽  
Canonical Ideal

The properties of the intersection algebra of two principal monomial ideals in a polynomial ring are investigated in detail. Results are obtained regarding the Hilbert series and the canonical ideal of the intersection algebra using methods from the theory of Diophantine linear equations with integer coefficients.

Short Generating Functions for some Semigroup Algebras

10.37236/1729 ◽  
2003 ◽  
Vol 10 (1) ◽  
Author(s):  
Graham Denham
Keyword(s):  
Rational Function ◽  
Generating Functions ◽  
Hilbert Series ◽  
Simple Expression ◽  
Arbitrary Field ◽  
Graded Algebra ◽  
Semigroup Algebras ◽  
Positive Integers

Let $a_1,\ldots,a_n$ be distinct, positive integers with $(a_1,\ldots,a_n)=1$, and let k be an arbitrary field. Let $H(a_1,\ldots,a_n;z)$ denote the Hilbert series of the graded algebra k$[t^{a_1},t^{a_2},\ldots,t^{a_n}]$. We show that, when $n=3$, this rational function has a simple expression in terms of $a_1,a_2,a_3$; in particular, the numerator has at most six terms. By way of contrast, it is known that no such expression exists for any $n\geq4$.

scholarly journals The Hilbert Series of a Linear Symplectic Circle Quotient

2014 ◽  
Vol 23 (1) ◽  
pp. 46-65 ◽  
Author(s):  
Hans-Christian Herbig ◽  
Christopher Seaton
Keyword(s):  
Hilbert Series

scholarly journals 2, 12, 117, 1959, 45171, 1170086, …: a Hilbert series for the QCD chiral Lagrangian

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Lukáš Gráf ◽  
Brian Henning ◽  
Xiaochuan Lu ◽  
Tom Melia ◽  
Hitoshi Murayama
Keyword(s):  
Hilbert Series ◽  
Charge Conjugation ◽  
External Fields ◽  
Dynkin Diagrams ◽  
Non Linear ◽  
Very High ◽  
Chiral Lagrangian

Abstract We apply Hilbert series techniques to the enumeration of operators in the mesonic QCD chiral Lagrangian. Existing Hilbert series technologies for non-linear realizations are extended to incorporate the external fields. The action of charge conjugation is addressed by folding the $$ \mathfrak{su}(n) $$ su n Dynkin diagrams, which we detail in an appendix that can be read separately as it has potential broader applications. New results include the enumeration of anomalous operators appearing in the chiral Lagrangian at order p8, as well as enumeration of CP-even, CP-odd, C-odd, and P-odd terms beginning from order p6. The method is extendable to very high orders, and we present results up to order p16.(The title sequence is the number of independent C-even and P-even operators in the mesonic QCD chiral Lagrangian with three light flavors of quarks, at chiral dimensions p2, p4, p6, …)

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