Synonyms for monomials or Related words with monomials
Examples of "monomials"
associated to standard Young tableaux.
For example, consider the
formula_10, formula_11, formula_12, and formula_13; the monomial orders above would order these four
All operations related to Gröbner bases require the choice of a total order on the
, with the following properties of compatibility with multiplication. For all
, , ,
that is sums of "divided power
" of the form
The number of
of degree at most in variables is formula_14 This follows from the one-to-one correspondence between the
of degree in variables and the
of degree at most in variables, which consists in substituting by 1 the extra variable.
coming from odd admissible sequences composed of k blocks.
in "n" variables define homogeneous functions . For example,
the permutation representations and the associated
are connected by
The simplest symmetric function containing all of these
by definition different
are orthogonal, so that
In mathematics, a moment matrix is a special symmetric square matrix whose rows and columns are indexed by
. The entries of the matrix depend on the product of the indexing
only (cf. Hankel matrices.)
In mathematics the monomial basis of a polynomial ring is its basis (as vector space or free module over the field or ring of coefficients) that consists in the set of all
form a basis because every polynomial may be uniquely written as a finite linear combination of
(this is an immediate consequence of the definition of a polynomial).
The polynomials of degree at most formula_13 form also a subspace, which has the
of degree at most formula_13 as a basis. The number of these
is the dimension of this subspace, equal to
The homogeneous polynomials of degree formula_13 form a subspace which has the
of degree formula_14 as a basis. The dimension of this subspace is the number of
of degree formula_13, which is
The Hilbert series is a compact way to express the number of
of a given degree: the number of
of degree in variables is the coefficient of degree of the formal power series expansion of
are called the
associated with formula_107 with respect to formula_6, resp. formula_12.
This is sometimes also called the homogeneity operator, because its eigenfunctions are the
formula_23, formula_24 are polynomials in formula_21 with positive coefficients
we have the following relations between the
and permutations corresponding to an element formula_40:
The theorem, in a special case, states that a necessary and sufficient condition for the
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