Related papers: The Bi-Musquash Conjecture

The usual concept of shape invariance is discussed and one extension of this concept is suggested.

We give a combinatorial characterization of conjugacy in the sylvester monoid (the monoid of binary search trees), showing that conjugacy is decidable for this monoid. We then prove that conjugacy is undecidable in general for homogeneous…

We show that bicovariant bimodules as defined by Woronowicz are in one to one correspondence with the Drinfeld quantum double representations. We then prove that a differential calculus associated to a bicovariant bimodule of dimension n is…

We define strict and weak duality involutions on 2-categories, and prove a coherence theorem that every bicategory with a weak duality involution is biequivalent to a 2-category with a strict duality involution. For this purpose we…

We formulate and discuss a conjecture which would extend a classical inequality of Bernstein.

We confirm several conjectures of Guo, Jouhet and Zeng concerning the factors of alternative binomials sums.

The authors developed in a recent paper natural dualities for finitely generated quasivarieties of Sugihara algebras. They thereby identified the admissibility algebras for these quasivarieties which, via the Test Spaces Method devised by…

In this paper, we give a survey of the recent develpoments of the DDVV conjecture.

A new representation of Dirac's delta-distribution, based on the so-called q-exponentials, has been recently conjectured. We prove here that this conjecture is indeed valid.

In this paper, we consider the poly-cauchy polynomials and numbers of the second kind which were studied by Komatsu in [10]. We note that the poly-Cauchy polynomials of the second kind are the special generalized Bernoulli polynomials of…

Recently, B\'{e}nyi and the second author introduced two combinatorial interpretations for symmetrized poly-Bernoulli polynomials. In the present study, we construct bijections between these combinatorial objects. We also define various…

The mix of two maniplexes is the minimal maniplex that covers both. This construction has many important applications, such as finding the smallest regular cover of a maniplex. If one of the maniplexes is an abstract polytope, a natural…

I settle a conjecture of Andrews related to the Alladi-Schur polynomials. In addition, I give further relations and implications to two families of polynomials related to the Alladi-Schur polynomials.

A bicomplex is a simple mathematical structure, in particular associated with completely integrable models. The conditions defining a bicomplex are a special form of a parameter-dependent zero curvature condition. We generalize the concept…

We build a variant of Collatz Conjecture for polynomials over $\mathbb{F}_2$ and we prove that it is solved. By the way, we give several examples.

This note gives an informal overview of the proof in our paper "Borel Conjecture and Dual Borel Conjecture", see arXiv:1105.0823.

We show that Gushel-Mukai fivefolds admit a multiplicative Chow-K\"unneth decomposition, in the sense of Shen-Vial. As a consequence, a certain tautological subring of the Chow ring of powers of these varieties injects into cohomology.

The notion of cartesian bicategory, introduced by Carboni and Walters for locally ordered bicategories, is extended to general bicategories. It is shown that a cartesian bicategory is a symmetric monoidal bicategory.

The representation of integral binary forms as sums of two squares is discussed and applied to establish the Manin conjecture for certain Ch\^atelet surfaces defined over the rationals.

Given a composition of two commutative squares, one well-known pullback lemma says that if both squares are pullbacks, then their composition is also a pullback; another well-known pullback lemma says that if the composed square is a…