A subset of the vertex set of a graph G, S ⊆ V (G), is a (k, τ)-regular set if it induces a k-regular subgraph of G and every vertex not in the subset has τ neighbors in it. This paper is a contribution to the given problem of existence of (k, τ)-regular sets associated with all distinct eigenvalues of integral strongly regular graphs. The minimal idempotents of the Bose-Mesner algebra of stron...

People trade thousands of non-fungible tokens (NFT) daily. The NFT prices are expressed in cryptocurrency, and it is volatile. As the interest NFTs changes, their vary with time too. Is there an immanent meter to order by value? Within a single collection, vector features–traits–characterizes NFT. construct rarity meters based on assumed value trait rarity. But this process lacks formalism. In ...

We give some observations on association schemes with a relation of valency 2 from the representation theory of Bose–Mesner algebras and the basic structure theory. One of the applications of these observations is the classi-cation of the association schemes with a non-symmetric relation of valency 2 if the cardinality of the point set is a product of two primes, and another is the proof of Li’...

A subset of the vertex set of a graph G, S ⊆ V (G), is a (k, τ)-regular set if it induces a k-regular subgraph of G and every vertex not in the subset has τ neighbors in it. This paper is a contribution to the given problem of existence of (k, τ)-regular sets associated with all distinct eigenvalues of integral strongly regular graphs. The minimal idempotents of the Bose-Mesner algebra of stron...

We build interacting Fock spaces from association schemes and set up quantum walks on the resulting regular graphs (distance-regular distance-transitive). The construction is valid for growing space well defined asymptotically graph. To realize in terms of anyons we switch to dual view identify corresponding modular tensor categories Bose–Mesner algebra. Informally, fusion ring induced by schem...

Abstract. In 1989, Vaughan Jones introduced spin models and showed that they could be used to form link invariants in two different ways—by constructing representations of the braid group, or by constructing partition functions. These spin models were subsequently generalized to so-called 4-weight spin models by Bannai and Bannai; these could be used to construct partition functions, but did no...

A t-(v, k, A) design is a pair (X, B), where 99 is a collection of subsets of size k (called blocks) from a set X of cardinality u such that every t-element subset of X is contained in exactly 1 blocks of B. If the blocks in GJ are not repeated, the design is said to be simple. It is easy to show that the minimum value of L for which a 3-(28,.5, A) design can possibly exist is 30. The existence...