相关论文: MacWilliams-type equivalence relations

The MPE (Most Probable Explanation) query plays an important role in probabilistic inference. MPE solution algorithms for probabilistic relational models essentially adapt existing belief assessment method, replacing summation with…

We study ideals and filters of posets and of pseudocomplemented posets and show a version of the Separation Theorem, known for ideals and filters in lattices and semilattices, within this general setting. We extend the concept of a *-ideal…

The `Weyl symmetric functions' studied here naturally generalize classical symmetric (polynomial) functions, and `Weyl bialternants,' sometimes also called Weyl characters, analogize the Schur functions. For this generalization, the…

Motivated by generalizing Khovanov's categorification of the Jones polynomial, we study functors $F$ from thin posets $P$ to abelian categories $\mathcal{A}$. Such functors $F$ produce cohomology theories $H^*(P,\mathcal{A},F)$. We find…

A divisibility relation between the generators of a square-free monomial ideal formally encodes the situation when one generator divides the least common multiple of some other generators. The divisibility relations contribute to the…

The linear code equivalence (LCE) problem is shown to be equivalent to the point set equivalence (PSE) problem, i.e., the problem to check whether two sets of points in a projective space over a finite field differ by a linear change of…

Mixture models on order relations play a central role in recent investigations of transitivity in binary choice data. In such a model, the vectors of choice probabilities are the convex combinations of the characteristic vectors of all…

Given a bivariate weight function defined on the positive quadrant of $\mathbb{R}^2$, we study polynomials in two variables orthogonal with respect to varying measures obtained by special modifications of this weight function. In…

A finite poset X carries a natural structure of a topological space. Fix a field k, and denote by D(X) the bounded derived category of sheaves of finite dimensional k-vector spaces over X. Two posets X and Y are said to be derived…

We introduce two partially ordered sets, $P^A_n$ and $P^B_n$, of the same cardinalities as the type-A and type-B noncrossing partition lattices. The ground sets of $P^A_n$ and $P^B_n$ are subsets of the symmetric and the hyperoctahedral…

The present note establishes the equivalence of Mac Williams identities for an additive code C and its dual to Polarized Riemann-Roch Conditions on their Zeta-functions. In such a way, the duality of additive codes appears to be a polarized…

We provide a systematic classification of multiparticle entanglement in terms of equivalence classes of states under stochastic local operations and classical communication (SLOCC). We show that such an SLOCC equivalency class of states is…

An $N$-free poset is a poset whose comparability graph does not embed an induced path with four vertices. We use the well-quasi-order property of the class of countable $N$-free posets and some labelled ordered trees to show that a…

Since MacWilliams proved the original identity relating the Hamming weight enumerator of a linear code to the weight enumerator of its dual code there have been many different generalizations, leading to the development of $m$-tuple support…

The human ability to flexibly reason using analogies with domain-general content depends on mechanisms for identifying relations between concepts, and for mapping concepts and their relations across analogs. Building on a recent model of…

In 1962, Jesse MacWilliams published a set of formulas for linear and abelian group codes that among other applications, were incredibly valuable in the study of self-dual codes. Now called the MacWilliams Identities, her results relate the…

In a previous paper we derived equivalence relations for pseudo-Wronskian determinants of Hermite polynomials. In this paper we obtain the analogous result for Laguerre and Jacobi polynomials. The equivalence formulas are richer in this…

We introduce the notion of p*-values (p*-variables), which generalizes p-values (p-variables) in several senses. The new notion has four natural interpretations: operational, probabilistic, Bayesian, and frequentist. A main example of a…

In this paper we combine ideas from tolerance orders with recent work on OC interval orders. We consider representations of posets by unit intervals $I_v$ in which the interval endpoints ($L(v)$ and $R(v)$) may be open or closed as well as…

For an elliptic curve $E$ defined over the field $\mathbb{C}$ of complex numbers, we classify all translates of elliptic curves in $E^3$ such that the $x$-coordinates satisfy a linear equation. This classification enables us to establish a…