This paper presents a descending method to classify Boolean functions in 7 variables under the action of affine general linear group. The classification determines number classes, set orbits representatives and generator stabilizer each representative. consists iteration process $$RM(k, m)/RM(r-1, m)$$ from that RM(k, m)/RM(r, m). We namely obtain classifications RM(4, 7)/RM(2, 7) RM(7, 7)/RM(3...

We investigate the admissible vector-valued modular forms having three independent characters and vanishing Wronskian index determine which ones correspond to genuine 2d conformal field theories. This is done by finding bilinear coset-type relations that pair them into meromorphic with central charges 8, 16, 24, 32 40. Such pairings allow us identify some definite CFTs rule out others. As a key...

Let G be a finite group and let K = x the conjugacy class of an element G. In this paper, it is proved that if N normal subgroup such coset union ? 1 (the inverse x), then ? ? are solvable. As application, we prove there exists natural number n ? 2 ? ,

A bstract We systemically study the Hecke relations and c = 8 k coset among 2d rational conformal field theories (RCFTs) with up to seven characters. propose that characters of any RCFT — unitary or non-unitary satisfying a holomorphic modular linear differential equation (MLDE) can be realized as either image respect theory. Benefited from recent results on bootstrap, we check this proposal fo...

We prove that every 2-transitive group has a property called the EKR-module property. This gives characterization of maximum intersecting sets permutations in group. Specifically, characteristic vector any set is linear combination vectors stabilizers points and their cosets. also consider when derangement graph connected subgroup or coset subgroup.

First we show that the cosets of a fuzzy ideal μ in a BCK-algebraX form another BCK-algebra  X/μ (called the fuzzy quotient BCK-algebra of X by μ). Also we show thatX/μ is a fuzzy partition of X and we prove several some isomorphism theorems. Moreover we prove that if the associated fuzzy similarity relation of a fuzzy partition P of a commutative BCK-algebra iscompatible, then P is a fuzzy quo...

We prove that the minimal base size for the permutation action of the sporadic simple Baby monster group B on the cosets of its 7th and 8th maximal subgroup is 3 and 2 respectively. Motivated by the large sizes of these permutation actions, we develop new computational methods to prove that an orbit is regular and to show that two orbits are disjoint.