相关论文: A congruence identity satisfied by m-permutable va…

The paper established sufficient conditions of predictability with degeneracy for the spectrum at $M$-periodically located isolated points on the unit circle. It is also shown that $m$-periodic subsequences of these sequences are also…

We introduce the notion of a nest-representable tolerance and show that some results from our former paper "From congruence identities to tolerance identities" [CT] can be extended to this more general setting.

The "Modularity Conjecture" is the assertion that the join of two nonmodular varieties is nonmodular. We establish the veracity of this conjecture for the case of linear idempotent varieties. We also establish analogous results concerning…

We derive two general transformations for certain basic hypergeometric series from the recurrence formulae for the partial numerators and denominators of two $q$-continued fractions previously investigated by the authors. By then…

We prove that a curious generating series identity implies Faber's intersection number conjecture (by showing that it implies a combinatorial identity already given in arXiv:1902.02742) and give a new proof of Faber's conjecture by directly…

It is known that any square matrix over any field F is congruent to its transpose. We show that they are also *congruent with respect to any nonidentity involution on F.

A metric algebra is a metric variant of the notion of $\Sigma$-algebra, first introduced in universal algebra to deal with algebras equipped with metric structures such as normed vector spaces. In this paper, we showed metric versions of…

We show that a locally finite variety which omits abelian types is self-regulating if and only if it has a compatible semilattice term operation. Such varieties must have a type-set {5}. These varieties are residually small and, when they…

We propose and prove a new polynomial identity that implies Schur's partition theorem. We give combinatorial interpretations of some of our expressions in the spirit of Kur\c{s}ung\"oz. We also present some related polynomial and $q$-series…

In this paper we characterize the monoid congruences of commutative semigroups by the help of the notion of the separator of subsets of semigroups. We show that every monoid congruence of a commutative semigroup S can be constructed by the…

In this paper, we describe a congruence property of solvable polynomials with coefficients in the Gaussian field Q(i).

We investigate to what extent persistent homology benefits from the properties of the usual homology theory.

Some applications of a result, which is proved recently, is considered. We first prove three determinantal identities concerning the binomial coefficient and Stirling numbers of the first and the second kind. We also easily obtain the…

We improve a known result on the strong consistency of M-estimates of the regression parameters in a linear model for independent and identically distributed random errors under some mild conditions.

We study the formalized v statement by allowing the occurrence of different arrays of quantifiers in it. We prove that for some specific arrays of quantifiers we get consistency statements that are S-equivalent to the original…

In this note, we present a curious $q$-series identity with applications to certain partitions with bounded part differences.

In this paper, we introduce a new type fuzzy boundary and study some related set theoretic identities. Further, this new type of fuzzy boundary is compared with different existing fuzzy boundaries.

We study compatible aggregation functions on a general bounded distributive lattice $L$, where the compatibility is related to the congruences on $L$. As a by-product, a new proof of an earlier result of G. Gr\"atzer is obtained. Moreover,…

We prove an explicit degree formula for certain unitary Deligne-Lusztig varieties. Combining with an alternative degree formula in terms of Schubert calculus, we deduce several algebraic combinatorial identities which may be of independent…

In this paper we derive some interesting identities arising from the orhtogonality of gegenbauer polynomials.