Monomial conjecture information

In commutative algebra, a field of mathematics, the monomial conjecture of Melvin Hochster says the following: Let A be a Noetherian local ring of Krull...

\{0\}} . Monomial conjecture on Noetherian local rings Existence of perfect cuboids and associated cuboid conjectures Pierce–Birkhoff conjecture: every...

normal or Cohen–Macaulay. Standard monomial theory can be used to prove Demazure's conjecture. Standard monomial theory proves the Kempf vanishing theorem...

factor is a monomial in the ψ i {\displaystyle \psi _{i}} , the first Chern classes of the n cotangent line bundles, as in Witten's conjecture. Let a 1 ...

the Macdonald polynomials become the sums over W orbits, which are the monomial symmetric functions when the root system has type A. If we put t = qα and...

Seshadri (1979) showed that Demazure's conjecture (for classical groups) follows from their work on standard monomial theory, and Peter Littelmann extended...

and with a special volume of the Michigan Mathematical Journal. Monomial conjecture Hochster, Melvin (1975). Topics in the homological theory of modules...

This topic later found applications in local cohomology, in the monomial conjecture, and other branches of commutative algebra. Zakeri was born in Urmia...

1\}^{n}\to \{0,1\}} is at least the square root of its degree, thus settling a conjecture posed by Nisan and Szegedy in 1992. The proof is notably succinct, given...

B. Shapiro, "Trees, parking functions, syzygies, and deformations of monomial ideals", Transactions of the American Mathematical Society 356 (8), pp...

monomials. Factor: An expression being multiplied. Linear factor: A factor of degree one. Coefficient: An expression multiplying one of the monomials...

in J (usual sum of vectors). In particular, the product of two monomials is a monomial whose exponent vector is the sum of the exponent vectors of the...

polytopes to simplicial spheres, the g-conjecture, which was resolved in 2018 by Karim Adiprasito. Square-free monomial ideal in a polynomial ring and Stanley–Reisner...

number of) gluing maps of monomials in ψ {\displaystyle \psi } and κ {\displaystyle \kappa } classes. These pushforwards of monomials (hereafter called basic...

over a field F {\displaystyle F} . Suppose that the coefficient of the monomial x 1 k 1 ⋯ x n k n {\displaystyle x_{1}^{k_{1}}\cdots x_{n}^{k_{n}}} in...

received his PhD in 1981 from Princeton University with thesis Arithmetic of Monomial Relations between the Periods of Abelian Varieties under the supervision...

number is prime or composite and this without relying on mathematical conjectures such as the generalized Riemann hypothesis. The proof is also notable...

{\displaystyle \lambda } a partition, let m λ {\displaystyle m_{\lambda }} be the monomial symmetric polynomial associated to λ {\displaystyle \lambda } . Consider...

V W X Y Z See also Abstract simplicial complex Addition chain Scholz conjecture Algebraic combinatorics Alternating sign matrix Almost disjoint sets Antichain...

linear Diophantine equation equates to a constant the sum of two or more monomials, each of degree one. An exponential Diophantine equation is one in which...

solve several conjectures in standard monomial theory and other areas. Seshadri, C. S. (1995), "The work of P. Littelmann and standard monomial theory", in...

{\displaystyle K_{n}} be the set of polynomials that are products of monomials ± z 1 c 1 … z n c n {\displaystyle \pm z_{1}^{c_{1}}\dots z_{n}^{c_{n}}}...

Dvir's proof of the Finite Field Kakeya Conjecture using the polynomial method. Finite Field Kakeya Conjecture: Let F q {\displaystyle \mathbb {F} _{q}}...

of the study of analytic singularity and proof by Ecalle of the Dulac conjectures. It constitutes a formal object, extending the field of exp-log functions...