A bstract We expand Hilbert series technologies in effective field theory for the inclusion of massive particles, enabling, among other things, enumeration operator bases non-linearly realized gauge theories. find that Higgs mechanism is manifest at level series, as expected partition function an S -matrix subject to Goldstone equivalence theorem. In addition vectors, we detail how massive, spi...

Sets of zero-dimensional ideals in the polynomial ring k[x,y] that share same leading term ideal with respect to a given ordering are known be affine spaces called Gröbner cells. Conca-Valla and Constantinescu parametrize such cells terms certain canonical Hilbert-Burch matrices for lexicographical degree-lexicographical orderings, respectively. In this paper, we give parametrization (x,y)-prim...

Multivariate public key cryptosystems (MPKC) are constructed based on the problem of solving multivariate quadratic equations (MQ problem). Among various schemes, UOV is an important signature scheme since it underlying some schemes such as MAYO, QR-UOV, and Rainbow which was a finalist NIST PQC standardization project. To analyze security scheme, necessary to first fall degree or for system po...

The denominator of the Hilbert series of a finitely generated R-module M does not always divide the denominator of the Hilbert series of R. For this reason, we define the universal denominator. The universal denominator of a module M is the least common multiple of the denominators of the Hilbert series of all submodules of M. The universal denominator behaves nicely with respect to short exact...