An instance I of Ring Grooming consists of m sets A1, A2, . . . , Am from the universe {0, 1, . . . , n − 1} and an integer g ≥ 2. The unrestricted variant of Ring Grooming, referred to as Unrestricted Ring Grooming, seeks a partition {P1, P2, . . . , Pk} of {1, 2, . . . , m} such that |Pi | ≤ g for each 1 ≤ i ≤ k and ∑k i=1 | ⋃ r∈Pi Ar | is minimized. The restricted variant of Ring Grooming, r...

Kornel Szlachányi [28] recently used the term skew-monoidal category for a particular laxi ed version of monoidal category. He showed that bialgebroids H with base ring R could be characterized in terms of skew-monoidal structures on the category of one-sided R-modules for which the lax unit was R itself. We de ne skew monoidales (or skew pseudo-monoids) in any monoidal bicategory M . These are...

We consider a finite group acting on a vector space and the corresponding skew group algebra generated by the group and the symmetric algebra of the space. This skew group algebra illuminates the resulting orbifold and serves as a replacement for the ring of invariant polynomials, especially in the eyes of cohomology. One analyzes the Hochschild cohomology of the skew group algebra using isomor...

This article discusses skew generalized quasi-cyclic codes over any finite field F with Galois automorphism θ. This is a generalization of quasi-cyclic codes and skew polynomial codes. These codes have an added advantage over quasi-cyclic codes since their lengths do not have to be multiples of the index. After a brief description of the skew polynomial ring F[x; θ], we show that a skew general...

Let A be a ring with identity, id="M2"> σ endomorphism of id="M3"> that maps the identity to itself, id="M4"> δ id="M5"> -derivation id="M6"> , and consider skew-polynomial id="M7"> X ; , . When id="M8"> is ...

Motivated by Stanley's conjecture on the multiplication of Jack symmetric functions, we prove a couple identities showing that skew functions are semi-invariant up to translation and rotation $\pi$ angle diagram. It follows that, in some special cases, coefficients with respect basis monomial polynomials nonnegative integer coefficients.

The title compound, C(20)H(19)N(3)O(3)·C(3)H(7)NO, was synthesized by the reaction of 6-amino-pyrimidine-2,4(1H,3H)-dione and 4-methyl-benzaldehyde with 5,5-dimethyl-1,3-cyclo-hexa-nedione in 1-butyl-3-methyl-imidazolium bromide at 363 K. The pyrimidine ring adopts a half-chair conformation while the six-membered ring fused to the pyridine ring adopts a skew-boat conformation. The dihedral angl...

Let [Formula: see text] be a group-type partial action of connected groupoid on ring and the corresponding skew ring. In first part this paper, we investigate relation several theoretic properties between text]. For second part, using that every Leavitt path algebra is isomorphic to obtained from text], characterize when group-type. such case, obtain algebras results general rings. Several exam...