Related papers: On certain spaces of lattice diagram determinants
We introduce a method for proving lower bounds on the efficacy of semidefinite programming (SDP) relaxations for combinatorial problems. In particular, we show that the cut, TSP, and stable set polytopes on $n$-vertex graphs are not the…
We give a polynomial delay algorithm, that for any graph $G$ and positive integer $k$, enumerates all connected induced subgraphs of $G$ of order $k$. Our algorithm enumerates each subgraph in at most…
Predicting the $B_s^0-\bar{B}_s^0$ width difference $\Delta\Gamma_s$ relies on the heavy quark expansion and on hadronic matrix elements of $\Delta B=2$ operators. We present the first lattice QCD results for matrix elements of the…
We study monomial-Cartesian codes (MCCs) which can be regarded as $(r,\delta)$-locally recoverable codes (LRCs). These codes come with a natural bound for their minimum distance and we determine those giving rise to $(r,\delta)$-optimal…
Let $(k,|\cdot|)$ be a complete and algebraically closed valued field extension of $(\mathbb{Q}_p,|\cdot|_p)$. Given a finite morphism $\varphi:\mathscr{D}_1\to \mathscr{D}_2$ of unit discs over $k$, a differential module $(M,D)$ on…
A. Mukhopadhyay, M. R. Murty and K. Srinivas (http://arxiv.org/abs/0808.0418) have recently studied various arithmetic properties of the discriminant $\Delta_n(a,b)$ of the trinomial $f_{n,a,b}(t) = t^n + at + b$, where $n \ge 5$ is a fixed…
We present the results of a first-principles theoretical study of the inclusive semileptonic decays of the $D_{s}$ meson. We performed a state-of-the-art lattice QCD calculation by taking into account all sources of systematic errors. A…
We present formulae for computing the Yamada polynomial of spatial graphs obtained by replacing edges of plane graphs, such as cycle-graphs, theta-graphs, and bouquet-graphs, by spatial parts. As a corollary, it is shown that zeros of…
For a left vector space V over a totally ordered division ring F, let Co(V) denote the lattice of convex subsets of V. We prove that every lattice L can be embedded into Co(V) for some left F-vector space V. Furthermore, if L is finite…
Computing derivatives of observables with respect to parameters of the theory is a powerful tool in lattice QCD, as it allows the study of physical effects not directly accessible in the original Monte Carlo simulation. Prominent examples…
Given positive integers m,n,s,t, let z(m,n,s,t) be the maximum number of ones in a (0,1) matrix of size m-by-n that does not contain an all ones submatrix of size s-by-t. We find a flexible upper bound on z(m,n,s,t) that implies the known…
We present first results on the axial and pseudoscalar $\Delta$ form factors. The analysis is carried out in the quenched approximation where statistical errors are small and the lattice set-up can be investigated relatively quickly. We…
In this paper in $W_2^{(m,m-1)}(0,1)$ space the problem of construction of optimal quadrature formula in the sense of Sard is considered and using S.L. Sobolev's method it is obtained new optimal quadrature formula of such type. For the…
In the present study, we consider the Extra-Membrane-Intra model (EMI) for the simulation of excitable tissues at the cellular level. We provide the (possibly large) system of partial differential equations (PDEs), equipped with ad hoc…
Similar to how standard Young tableaux represent paths in the Young lattice, Latin rectangles may be use to enumerate paths in the poset of semi-magic squares with entries zero or one. The symmetries associated to determinant preserve this…
The purpose of this article is to investigate the combinatorial properties of the cross section lattice of a $J$-irreducible monoid associated with a semisimple algebraic group of one of the types $A_n$, $B_n$, or $C_n$. Our main tool is a…
We study the tiling of a two-dimensional region of the plane by $K$-cell one-dimensional tiles, or $K$-mers. Unlike previous studies, which typically allowed for one single value of $K$ or sometimes a small assortment of fixed values, here…
We determine the general structure of the partition function of the $q$-state Potts model in an external magnetic field, $Z(G,q,v,w)$ for arbitrary $q$, temperature variable $v$, and magnetic field variable $w$, on cyclic, M\"obius, and…
I review the lattice formulations of vector-like gauge theories (e.g. QCD) with domain-wall/overlap fermions, and discuss how to optimize the chiral symmetry for any finite $ N_s $ (sites in the fifth dimension). In this formulation, quark…
We analyze the factorization process for lattice maps, searching for integrable cases. The maps were assumed to be at most quadratic in the dependent variables, and we required minimal factorization (one linear factor) after 2 steps of…