scholarly journals An algebraic proof of determinant formulas of Grothendieck polynomials

2017 ◽  
Vol 93 (8) ◽  
pp. 82-85 ◽  
Author(s):  
Tomoo Matsumura
Keyword(s):  
Algebraic Proof ◽  
Grothendieck Polynomials

scholarly journals Set-valued Rothe tableaux and Grothendieck polynomials

2021 ◽  
Vol 128 ◽  
pp. 102203
Author(s):  
Neil J.Y. Fan ◽  
Peter L. Guo
Keyword(s):  
Grothendieck Polynomials

scholarly journals Identities on factorial Grothendieck polynomials

2019 ◽  
Vol 111 ◽  
pp. 101933 ◽  
Author(s):  
Peter L. Guo ◽  
Sophie C.C. Sun
Keyword(s):  
Grothendieck Polynomials

A resolution of the Euler operator II

1981 ◽  
Vol 89 (3) ◽  
pp. 501-510 ◽  
Author(s):  
Chehrzad Shakiban
Keyword(s):  
Calculus Of Variations ◽  
Differential Polynomials ◽  
Algebraic Proof ◽  
Lagrange Equations ◽  
Partial Differential ◽  
Independent Variables ◽  
Several Variables ◽  
Euler Operator ◽  
Dependent Variables ◽  
Local Exactness

AbstractAn exact sequence resolving the Euler operator of the calculus of variations for partial differential polynomials in several dependent and independent variables is described. This resolution provides a solution to the ‘Inverse problem of the calculus of variations’ for systems of polynomial partial equations.That problem consists of characterizing those systems of partial differential equations which arise as the Euler-Lagrange equations of some variational principle. It can be embedded in the more general problem of finding a resolution of the Euler operator. In (3), hereafter referred to as I, a solution of this problem was given for the case of one independent and one dependent variable. Here we generalize this resolution to several independent and dependent variables simultaneously. The methods employed are similar in spirit to the algebraic techniques associated with the Gelfand-Dikii transform in I, although are considerably complicated by the appearance of several variables. In particular, a simple algebraic proof of the local exactness of a complex considered by Takens(5), Vinogradov(6), Anderson and Duchamp(1), and others appears as part of the resolution considered here.

A completeness theorem for higher order logics

2000 ◽  
Vol 65 (2) ◽  
pp. 857-884 ◽  
Author(s):  
Gábor Sági
Keyword(s):  
Set Theory ◽  
Representation Theorem ◽  
Completeness Theorem ◽  
Higher Order ◽  
Algebraic Solution ◽  
Algebraic Proof ◽  
Relation Algebras ◽  
Cylindric Algebras ◽  
Strong Representation ◽  
Algebraic Counterpart

AbstractHere we investigate the classes of representable directed cylindric algebras of dimension α introduced by Németi [12]. can be seen in two different ways: first, as an algebraic counterpart of higher order logics and second, as a cylindric algebraic analogue of Quasi-Projective Relation Algebras. We will give a new, “purely cylindric algebraic” proof for the following theorems of Németi: (i) is a finitely axiomatizable variety whenever α ≥ 3 is finite and (ii) one can obtain a strong representation theorem for if one chooses an appropriate (non-well-founded) set theory as foundation of mathematics. These results provide a purely cylindric algebraic solution for the Finitization Problem (in the sense of [11]) in some non-well-founded set theories.

scholarly journals An algebraic proof of the real number PCP theorem

2017 ◽  
Vol 40 ◽  
pp. 34-77 ◽  
Author(s):  
Martijn Baartse ◽  
Klaus Meer
Keyword(s):  
Real Number ◽  
Algebraic Proof ◽  
The Real ◽  
Pcp Theorem

scholarly journals On the Decidability of Intuitionistic Tense Logic without Disjunction

2020 ◽  
Author(s):  
Fei Liang ◽  
Zhe Lin
Keyword(s):  
Proof Theory ◽  
Tense Logic ◽  
Heyting Algebras ◽  
Finite Model ◽  
Algebraic Proof ◽  
Model Property ◽  
Algebraic Models ◽  
Finite Axiomatizability ◽  
Finite Model Property ◽  
Modal Operators

Implicative semi-lattices (also known as Brouwerian semi-lattices) are a generalization of Heyting algebras, and have been already well studied both from a logical and an algebraic perspective. In this paper, we consider the variety ISt of the expansions of implicative semi-lattices with tense modal operators, which are algebraic models of the disjunction-free fragment of intuitionistic tense logic. Using methods from algebraic proof theory, we show that the logic of tense implicative semi-lattices has the finite model property. Combining with the finite axiomatizability of the logic, it follows that the logic is decidable.

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