Related papers: Plactic monoids satisfy nontrivial identities
We present some identities dealing with reflexive and admissible relations and which, through a variety, are equivalent to congruence modularity.
We prove that there exists a constant $c>0$ such that any finite group having no non-trivial mixed identity of length $\leq c$ is an almost simple group with a simple group of Lie type as its socle. Starting the study of mixed identities…
In answer to a question of P. Hall, we supply another construction of a group which is isomorphic to each of its non-trivial normal subgroups.
We prove some trigonometric identities involving Chebyshev polynomials of second kind. The identities were inspired by atomic form factor calculations. Generalizations of these identities, if found, will help to increase the numerical…
We show that any nonlinear field theory giving rise to static solutions with finite energy like, e.g., topological solitons, allows us to derive an infinite number of integral identities which any such solution has to obey. These integral…
We exhibit a 6-element semigroup that has no finite identity basis but nevertheless generates a variety whose finite membership problem admits a polynomial algorithm.
In this note, we will give a short proof of an identity for cubic partitions.
A number of properties of spherical Artin groups extend to Garside groups, defined as the groups of fractions of monoids where least common multiples exist, there is no nontrivial unit, and some additional finiteness conditions are…
Presentations for unbraided, braided and symmetric pseudomonoids are defined. Biequivalences characterising the semistrict bicategories generated by these presentations are proven. It is shown that these biequivalences categorify results in…
We prove that non-pretentious multiplicative functions are orthogonal to polynomials over $\mF_q[x]$ (up to characteristic conditions).
An additive submonoid of the nonnegative cone of the real line is called a positive monoid. Positive monoids consisting of rational numbers (also known as Puiseux monoids) have been the subject of several recent papers. Moreover, those…
We present a generalization of the Newton-Girard identities, along with some applications. As an addendum, we collect many evaluations of symmetric polynomials to which these identities apply.
In this paper, we show that the infinitesimal dilogarithm and Kontsevich's one-and-a-half logarithm function satisfies the identities which result from periods in cluster patterns. We also prove that these cluster identities are a…
For the Schur polynomials bounded and unbounded generalizations of the Cauchy identities are found.
We describe overcommutative varieties of semigroups whose lattice of overcommutative subvarieties satisfies a non-trivial identity or quasiidentity. These two properties turn out to be equivalent.
We construct explicit non-isotrivial families of polynomials over $\mathbb{Q}$ satisfying uniform boundedness for their rational preperiodic points.
I characterize the combinatorially complete pargoids (partial applicative systems) by expandability with two constants that satisfy the well-known identities. An example shows that this class contains more than just the reducts of partial…
We survey results devoted to the lattice of varieties of monoids. Along with known results, some unpublished results are given with proofs. A number of open questions and problems are also formulated.
In this paper we establish two symmetric identities on sums of products of Euler polynomials.
In this paper, we investigate some properties of Chebyshev polynomials arising from non-linear differential equations. From our investigation, we derive some new and interesting identities on Chebyshev polynomials.