Related papers: Fomin-Greene monoids and Pieri operations
We consider the problem of random uniform generation of traces (the elements of a free partially commutative monoid) in light of the uniform measure on the boundary at infinity of the associated monoid. We obtain a product decomposition of…
A linking pairing is a symetric bilinear pairing lambda: GxG --> Q/Z on a finite abelian group. The set of isomorphism classes of linking pairings is a non-cancellative monoid E under orthogonal sum, which is infinitely generated and…
This is the first of a series of papers in which we initiate and develop the theory of reflection monoids, motivated by the theory of reflection groups. The main results identify a number of important inverse semigroups as reflection…
Consider the algebra Q<<x_1,x_2,...>> of formal power series in countably many noncommuting variables over the rationals. The subalgebra Pi(x_1,x_2,...) of symmetric functions in noncommuting variables consists of all elements invariant…
In this short paper, the commutator of monomials of operators obeying constant commutation relations is expressed in terms of anticommutators. The formula involves Bernoulli numbers or Euler polynomials evaluated in zero. The role of…
Poizat's construction of theories of fields with a multiplicative subgroup of green points is extended in several directions: First, we also construct similar theories where the green points form a divisible…
We exactly solve the ferromagnetic spin-1/2 Ising model on the Bethe lattice in the presence of an external magnetic field by means of the equations of motion method within the Green's function formalism. In particular, such an approach is…
The super Macdonald polynomials indexed by the super partitions form a basis of the level zero super Fock module (combinatorial representation) of the quantum toroidal algebra $\mathcal{U}_{q,t}(\widehat{\widehat{\mathfrak{gl}}}_{1|1})$.…
The notion of symmetry in polynomial rings with several indeterminates is generalized to polynomial rings over finite fields. Families of extensions of the projective line over a finite field of constants possessing this property are…
We prove a conjecture of Bourn and Willenbring (2020) regarding the palindromicity and unimodality of a certain family of polynomials $N_n(t)$. These recursively defined polynomials arise as the numerators of generating functions in the…
We present a complete logic for reasoning with functional dependencies (FDs) with semantics defined over classes of commutative integral partially ordered monoids and complete residuated lattices. The dependencies allow us to express…
A certain analysis of all possible associative binary operations on N is presented. This is equivalent with an analysis of all possible monoid structures on N. Several results and a conjecture in this regard are given.
Every $F$-inverse monoid can be equipped with the unary operation which maps each element to the maximum element of its $\sigma$-class. In this enriched signature, the class of all $F$-inverse monoids forms a variety of algebraic…
We focus on (partial) functions that map input strings to a monoid such as the set of integers with addition and the set of output strings with concatenation. The notion of regularity for such functions has been defined using two-way…
By establishing relations between operators on compositions, we show that the posets of compositions arising from the right and left Pieri rules for noncommutative Schur functions can each be endowed with both the structure of dual graded…
We investigate the algebraic structure on the set of closure operations of a ring. We show the set of closure operations is not a monoid under composition for a discrete valuation ring. Even the set of semiprime operations over a DVR is not…
Numerical monoids (cofinite, additive submonoids of the non-negative integers) arise frequently in additive combinatorics, and have recently been studied in the context of factorization theory. Arithmetical numerical monoids, which are…
In this note, we consider the monoid $\mathcal{PIM}_{n}$ of all partial monotone transformations on a chain with $n$ elements whose domains and ranges are intervals and its submonoid $\mathcal{IM}_{n}$ constituted by the full…
We study the Gnedin-Kingman graph, which corresponds to Pieri's rule for the monomial basis $\{M_{\lambda}\}$ in the algebra $\mathrm{QSym}$ of quasisymmetric functions. The paper contains a detailed announcement of results concerning the…
In this paper we study the complex symmetry in the several variable Fock space by using the techniques of weighted composition operators and semigroups. We characterize unbounded weighted composition operators that are (real) complex…