相关论文: Avoiding maximal parabolic subgroups of S_k

For any involution $\sigma$ of a semisimple Lie algebra $\mathfrak g$, one constructs a non-reductive Lie algebra $\mathfrak k$, which is called a $\mathbb Z_2$-contraction of $\mathfrak g$. In this paper, we attack the problem of…

It is shown that the sequence of rational numbers $r(k)$ generated by the ordinary generating function $\prod_{k=1}^\infty (1+x^k/k)$ converges to a limit $C > 0$. $C$ can be expressed as $C = \exp\Bigl(-\sum_{k = 2}^\infty…

Using reduction of spherical functions, we obtain generators of the algebra and the field of invariants for the coadjoint representation of Borel and maximal nilpotent subalgebras of simple Lie algebras.

Machines whose main purpose is to permute and sort data are studied. The sets of permutations that can arise are analysed by means of finite automata and avoided pattern techniques. Conditions are given for these sets being enumerated by…

Generating functions for a fixed genus map and hypermap enumeration become rational after a simple explicit change of variables. Their numerators are polynomials with integer coefficients that obey a differential recursion, and denominators…

A procedure is described that makes use of the generating function of characters to obtain a new generating function $H$ giving the multiplicities of each weight in all the representations of a simple Lie algebra. The way to extract from…

Motivated by the concept of "generating operators" for a countable family of operators introduced in the recent paper (arXiv:2306.16800), we find a method to reconstruct the Rankin--Cohen brackets from a very simple multivariable contour…

Let $m,k$ be fixed positive integers. Determining the generating function for the number of tilings of an $m\times n$ rectangle by $k\times 1$ rectangles is a long-standing open problem to which the answer is only known in certain special…

We find the generating function for the class of all permutations that avoid the patterns 3124 and 4312 by showing that it is an inflation of the union of two geometric grid classes.

Given a connected simply connected semisimple group G and a connected spherical subgroup K we determine the generators of the extended weight monoid of G/K, based on the homogeneous spherical datum of G/K. Let H be a reductive subgroup of G…

We call a family G of subsets of [n] a k-generator of (\mathbb{P}[n]) if every (x \subset [n]) can be expressed as a union of at most k disjoint sets in (\mathcal{G}). Frein, Leveque and Sebo conjectured that for any (n \geq k), such a…

In this paper we derive the generating function of RNA structures with pseudoknots. We enumerate all $k$-noncrossing RNA pseudoknot structures categorized by their maximal sets of mutually intersecting arcs. In addition we enumerate…

For a fixed positive integer $k$, any element $g$ of the permutation group $S_{k}$ acts on the tensor product vertex operator algebra $V^{\otimes k}$ in the obvious way. In this paper, we determine the $S$-matrix of $\left(V^{\otimes…

We examine two different ways of encoding a counting function, as a rational generating function and explicitly as a function (defined piecewise using the greatest integer function). We prove that, if the degree and number of input…

Snakes are analogues of alternating permutations defined for any Coxeter group. We study these objects from the point of view of combinatorial Hopf algebras, such as noncommutative symmetric functions and their generalizations. The main…

For each fully commutative permutation, we construct a "boolean core," which is the maximal boolean permutation in its principal order ideal under the right weak order. We partition the set of fully commutative permutations into the…

We find the exponential generating function for permutations with all valleys even and all peaks odd, and use it to determine the asymptotics for its coefficients, answering a question posed by Liviu Nicolaescu. The generating function can…

We study the distribution of the number of permutations with a given periodic up-down sequence w.r.t. the last entry, find exponential generating functions and prove asymptotic formulas for this distribution.

Let $A_k$ be the set of permutations in the symmetric group $S_k$ with prefix 12. This paper concerns the enumeration of involutions which avoid the set of patterns $A_k$. We present a bijection between symmetric Schroder paths of length…

A solution is proposed for the problem of composition of ordinary generating functions. A new class of functions that provides a composition of ordinary generating functions is introduced; main theorems are presented; compositae are written…