Related papers: Asymptotics of 3-stack-sortable permutations

Extending earlier work, we find the two-loop term in the beta-function for the scalar coupling $\zeta$ in a generalized Wilson loop operator of the $\mathcal{N}=4$ SYM theory, working in the planar weak-coupling expansion. The beta-function…

The contraction semigroup $S(t)={\rm e}^{t\mathbb{A}}$ generated by the abstract linear dissipative evolution equation $$ \ddot u + A u + f(A) \dot u=0 $$ is analyzed, where $A$ is a strictly positive selfadjoint operator and $f$ is an…

In this paper we use generating function methods to obtain new asymptotic results about spaces of $F$-stable maximal tori in $GL_n(\overline{F_q})$, $Sp_{2n}(\overline{F_q})$, and $SO_{2n+1}(\overline{F_q})$. We recover stability results of…

In [Temme N.M., Special functions. An introduction to the classical functions of mathematical physics, A Wiley-Interscience Publication, John Wiley & Sons, Inc., New York, 1996, Section 11.3.3.1] a uniform asymptotic expansion for the…

Let $k\ge 2$ be an integer and let $A$ be a set of nonnegative integers. The representation function $R_{A,k}(n)$ for the set $A$ is the number of representations of a nonnegative integer $n$ as the sum of $k$ terms from $A$. Let $A(n)$…

We study the number of random permutations needed to invariably generate the symmetric group, $S_n$, when the distribution of cycle counts has the strong $\alpha$-logarithmic property. The canonical example is the Ewens sampling formula,…

In this paper we study the well-posedness of the evolution equation of the form $u'(t)=Au(t)+Cu(t)$, $t\ge 0$, where $A$ is the generator of a $C_0$- semigroup and $C$ is a (possibly unbounded) linear operator in a Banach space…

We evaluate combinatorially certain connection coefficients of the symmetric group that count the number of factorizations of a long cycle as a product of three permutations. Such factorizations admit an important topological interpretation…

We study new statistics on permutations that are variations on the descent and the inversion statistics. In particular, we consider the alternating descent set of a permutation sigma = sigma_1sigma_2...sigma_n defined as the set of indices…

Defining a family of recurrences, we generalize Comtet's formula for the generating function of the enumeration of indecomposable permutations. Consequently, we generalize Panaitopol's asymptotic expansion for the prime counting function,…

Consider a supercritical Crump--Mode--Jagers process such that all births are at integer times (the lattice case). Let $\widehat\mu(z)$ be the generating function of the intensity of the offspring process, and consider the complex roots of…

The algebraic properties of formal power series, whose coefficients show factorial growth and admit a certain well-behaved asymptotic expansion, are discussed. It is shown that these series form a subring of $\mathbb{R}[[x]]$. This subring…

We propose explicit expressions for the form factors, including their normalization constants, of topologically charged (or soliton-creating) operators in the sine-Gordon model. The normalization constants, which constitute the main content…

Asymptotic behavior of the anomalous dimensions of Wilson operators with high spin and twist is governed in planar N=4 SYM theory by the scaling function which coincides at strong coupling with the energy density of a two-dimensional…

Let $F_0=\mathbf Q(\sqrt{-d})$ be an imaginary quadratic field with $3\nmid d$ and let $K_0=\mathbf Q(\sqrt{3d})$. Let $\varepsilon_0$ be the fundamental unit of $K_0$ and let $\lambda$ be the Iwasawa $\lambda$-invariant for the cyclotomic…

We show that the growth of the principal M\"obius function on the permutation poset is exponential. This improves on previous work, which has shown that the growth is at least polynomial. We define a method of constructing a permutation…

We compute the beta functions for the $O(N)^3$-invariant general sextic tensor model up to cubic order in the coupling constant, and at leading order in the $1/N$ expansion. Our method is a direct, explicit one, in the sense that we…

Enhanced tensor field theories (eTFT) have dominant graphs that differ from the melonic diagrams of conventional tensor field theories. They therefore describe pertinent candidates to escape the so-called branched polymer phase, the…

We obtain an asymptotic expansion for $p(n)$, the number of partitions of a natural number $n$, starting from a formula that relates its generating function $f(t), t\in (0,1)$ with the characteristic functions of a family of sums of…

We calculate the third coefficient of the lattice beta function associated with the Wilson formulation for both gauge fields and fermions. This allows us to evaluate the three-loop correction (linear in $g_0^2$) to the relation between the…