相关论文: Path generating transforms

We introduce a family of deformed Bailey pairs whose $q$-series, which converge in a two-step limit ($q \to 1^-$ followed by $n \to \infty$) to Dirichlet $L$-functions scaled by $1/\sqrt{\pi}$. This construction generalizes to arbitrary…

The interlace polynomials introduced by Arratia, Bollobas and Sorkin extend to invariants of graphs with vertex weights, and these weighted interlace polynomials have several novel properties. One novel property is a version of the…

We consider paths in the plane with $(1,0),$ $(0,1),$ and $(a,b)$-steps that start at the origin, end at height $n,$ and stay to the left of a given non-decreasing right boundary. We show that if the boundary is periodic and has slope at…

Marco Buratti's conjecture states that if $p$ is a prime and $L$ a multiset containing $p-1$ non-zero elements from the integers modulo $p$, then there exists a Hamiltonian path in the complete graph of order $p$ with edge lengths in $L$.…

Quadratic relations of the intertwiners are given explicitly in two cases of chiral conformal field theory, and monomial bases of the representation spaces are constructed by using the Fourier components of the intertwiners. The two cases…

We consider the continuum scaling limit of the infinite series of Yang-Baxter integrable logarithmic minimal models LM(p,p') as `rational' logarithmic conformal field theories with extended W symmetry. The representation content is found to…

We consider the monomial expansion of the $q$-Whittaker and modified Hall-Littlewood polynomialsarising from specialization of the modified Macdonald polynomial. The two combinatorial formulas for the latter due to Haglund, Haiman, and…

We study heaps of pieces for lattice paths, which give a combinatorial visualization of lattice paths. We introduce two types of heaps: type $I$ and type $II$. A heap of type $I$ is characterized by peaks of a lattice path. We have a…

Let $p$ be a prime number and $\left(\frac{\cdot}{p}\right)$ be the Legendre symbol modulo $p$. The \emph{Legendre path} attached to $p$ is the polygonal path whose vertices are the normalized character sums $\frac{1}{\sqrt{p}} \sum_{n\leq…

An $\mathbb{F}_q$-linear set of rank $k$ on a projective line $\mathrm{PG}(1,q^h)$, containing at least one point of weight one, has size at least $q^{k-1}+1$ (see [J. De Beule and G. Van De Voorde, The minimum size of a linear set, J.…

We show that for polytopes P_1, P_2, ..., P_r \subset \R^d, each having n_i \ge d+1 vertices, the Minkowski sum P_1 + P_2 + ... + P_r cannot achieve the maximum of \prod_i n_i vertices if r \ge d. This complements a recent result of Fukuda…

Let $f$ be a Hecke-Maass cusp form for $SL_3(\mathbb{Z})$ and $\chi$ a primitive Dirichlet character of prime power conductor $\mathfrak{q}=p^{\kappa}$ with $p$ prime and $\kappa\geq 10$. We prove a subconvexity bound $$…

We consider several families of combinatorial polytopes associated with the following NP-complete problems: maximum cut, Boolean quadratic programming, quadratic linear ordering, quadratic assignment, set partition, set packing, stable set,…

Studying the virtual Euler characteristic of the moduli space of curves, Harer and Zagier compute the generating function $C_g(z)$ of unicellular maps of genus $g$. They furthermore identify coefficients, $\kappa^{\star}_{g}(n)$, which…

Lusztig $q$-weight multiplicities extend the Kostka-Foulkes polynomials to a broader range of Lie types. In this work, we investigate these multiplicities through the framework of Kirillov-Reshetikhin crystals. Specifically, for type $C$…

The Lie superalgebra q(2) and its class of irreducible representations V_p of dimension 2p (p being a positive integer) are considered. The action of the q(2) generators on a basis of V_p is given explicitly, and from here two realizations…

We investigate Laplace type and Laplace-Stieltjes type multipliers in the $d$-dimensional setting of the Dunkl harmonic oscillator with the associated group of reflections isomorphic to $\mathbb{Z}_2^d$ and in the related context of…

This is the first paper that provides a systematic treatment of the $r$-dimensional PTE problem in additive number theory, abbreviated by PTE$_r$, through its connection with combinatorial design theory, the branch of combinatorial…

This is a continuation of our combinatorial program on the enumeration of Borel orbits in symmetric varieties of classical types. Here, we determine the generating series the numbers of Borel orbits in…

Recently, the authors gave Ramsey-type results for the path cover/partition number of graphs. In this paper, we continue the research about them focusing on digraphs, and find a relationship between the path cover/partition number and…