Related papers: A natural generalization of Balanced Tableaux
Matrix congruence can be used to mimic linear maps between homogeneous quadratic polynomials in $n$ variables. We introduce a generalization, called standard-form congruence, which mimics affine maps between non-homogeneous quadratic…
In this paper, we define generalized braid theories in alignment with the language of Fenn and Bartholomew for knot theories, and compute a generating set for the pure generalized braid theories. Using this, we prove that every oriented…
We prove K-theoretic and shifted K-theoretic analogues of the bijection of Stanton and White between domino tableaux and pairs of semistandard tableaux. As a result, we obtain product formulas for pairs of stable Grothendieck polynomials…
We take a unifying and new approach toward polynomial and trigonometric approximation in an arbitrary number of variables, resulting in a precise and general ready-to-use tool that anyone can easily apply in new situations of interest. The…
We discuss how canonical and universal constructions, properties and characterizations interact with equality in the framework of Homotopy Type Theory, comparing it with Grothendieck's use of equality and shedding further light on…
A little-known and highly economical characterization of the real interval [0, 1], essentially due to Freyd, states that the interval is homeomorphic to two copies of itself glued end to end, and, in a precise sense, is universal as such.…
The supercharacter theory of algebra groups gave us a representation theoretic realization of the Hopf algebra of symmetric functions in noncommuting variables. The underlying representation theoretic framework comes equipped with two…
We define a general class of dependent type theories, encompassing Martin-L\"of's intuitionistic type theories and variants and extensions. The primary aim is pragmatic: to unify and organise their study, allowing results and constructions…
Permutation tableaux are combinatorial objects related with permutations and various statistics on them. They appeared in connection with total positivity in Grassmannians, and stationary probabilities in a PASEP model. In particular they…
We introduce a new notion of "regularity structure" that provides an algebraic framework allowing to describe functions and / or distributions via a kind of "jet" or local Taylor expansion around each point. The main novel idea is to…
We extend work of McKay, Morse, and Wilf by giving exact formulas and asymptotic formulas for the number of skew Young tableaux T in two situations: (1) the "inside shape" and total number of cells of T are fixed, and (2) the inside shape…
The paper is a contribution both to the theoretical foundations and to the actual construction of efficient automatizable proof procedures for non-classical logics. We focus here on the case of finite-valued logics, and exhibit: (i) a…
Based on the theory of Fermat reals we introduce new topologies on spaces of Colombeau generalized points and derive some of their fundamental properties. In particular, we obtain metric topologies on the space of near-standard generalized…
We introduce a special class of real semiflows, which is used to define a general type of evolution semigroups, associated to not necessarily exponentially bounded evolution families. Giving spectral characterizations of the corresponding…
We present a tableau calculus for reasoning in fragments of natural language. We focus on the problem of pronoun resolution and the way in which it complicates automated theorem proving for natural language processing. A method for…
We introduce a remarkable new family of norms on the space of $n \times n$ complex matrices. These norms arise from the combinatorial properties of symmetric functions, and their construction and validation involve probability theory,…
A generalized definition of the determinant of matrices is given, which is compatible with the usual determinant for square matrices and keeps many important properties, such as being an alternating multilinear function, keeping…
In this paper, we find bounds for the eigenvalues of matrix polynomials. In particular, we find generalizations of Cauchy's classical Theorem for distribution of eigenvalues of matrix polynomial.
We derive combinatorial identities, involving the Bernoulli and Euler numbers, for the numbers of standard Young tableaux of certain skew shapes. This generalizes the classical formulas of D. Andre on the number of up-down permutations. The…
Expanding upon recent work, a new class of $A$-functions is introduced that can be viewed as an appropriate generalization of the class of regular $A$-functions, the class of structured $A$-functions, and the class of perfect $A$-functions.…