We prove an identity conjectured by Adin and Roichman involving the descent set of λ-unimodal cyclic permutations. These permutations appear in the character formulas for certain representations of the symmetric group and these formulas are usually proven algebraically. Here, we give a combinatorial proof for one such formula and discuss the consequences for the distribution of the descent set ...

Given an integer s ≥ 0 and a permutation π ∈ Sn, let Γπ,s be the graph on n vertices {1, . . . , n} where two vertices i < j are adjacent if the permutation flips their order and there are at most s integers k, i < k < j, such that π = [. . . j . . . k . . . i . . .]. In this short paper we determine the maximum number of edges in Γπ,s for all s ≥ 1 and characterize all permutations π which ach...

Adin, Brenti, and Roichman [Adv. in Appl. Math. 27 (2001), 210–224], in answering a question posed by Foata, introduced two descent numbers and major indices for the hyperoctahedral group Bn, whose joint distribution generalizes an identity due to MacMahon and Carlitz. We shall show that yet another pair of statistics exists, and whose joint distribution constitutes a “natural” solution to Foat...

Several methods were used for the evaluation of feed protein for rumen degradability and intestinal digestibility of rumen undegraded protein (RUP). The aim of this work was to explore the possibility of using the Cornell method of predicting the fraction RUP. An in situ method was adopted for estimation of degradability parameters (a, b, c) and effective degradable crude protein (EDCP), and fi...

O texto problematiza a atuação do Conselho Federal de Educação Física e seus Conselhos Regionais (CONFEF/CREF) na defesa dos trabalhadores(as) da (EF). Parte duas perguntas: que é Ação Inconstitucionalidade (ADIn) nº 3.428/2005, sua origem, seu desenvolvimento estágio atual; o CONFEF/CREF (in)capacidade proteger os trabalhadores(as)? Objetiva subsidiar as posições Movimento Nacional Contra Regu...

We prove tight lower bounds for the coefficients of the generalized h-vector of a rational polytope with a symmetry of prime order that is fixed–point–free on the boundary. These bounds generalize results of R. Stanley and R. Adin for the h–vector of a simplicial rational polytope with a central symmetry or a symmetry of prime order respectively.

The Gelfand representation of $${\mathcal {S}}_n$$ is the multiplicity-free direct sum irreducible representations . In this paper, we use a result Adin, Postnikov, and Roichman to find generating function for character. order function, investigate descents so-called $$\lambda $$ -unimodal involutions.