Signed combinatorial interpretations in algebraic combinatorics [PDF]
Algebraic CombinatoricsWe prove the existence of signed combinatorial interpretations for several large families of structure constants. These families include standard bases of symmetric and quasisymmetric polynomials, as well as various bases in Schubert theory.
Igor Pak, Colleen Robichaux
openalex +2 more sources
Poset topology and homological invariants of algebras arising in algebraic combinatorics [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 We present a beautiful interplay between combinatorial topology and homological algebra for a class of monoids that arise naturally in algebraic combinatorics. We explore several applications of this interplay.
Stuart Margolis +2 more
doaj +6 more sources
Asymptotics of lattice walks via analytic combinatorics in several variables [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 We consider the enumeration of walks on the two-dimensional non-negative integer lattice with steps defined by a finite set S ⊆ {±1, 0}2 . Up to isomorphism there are 79 unique two-dimensional models to consider, and previous work in this area has used ...
Stephen Melczer, Mark C. Wilson
doaj +8 more sources
Algebraic combinatorial geometry: the polynomial method in arithmetic combinatorics, incidence combinatorics, and number theory [PDF]
, 2013 Arithmetic combinatorics is often concerned with the problem of bounding the behaviour of arbitrary finite sets in a group or ring with respect to arithmetic operations such as addition or multiplication.
Terence Tao
openalex +3 more sources
Applications of Algebraic Combinatorics to Algebraic Geometry [PDF]
Indagationes mathematicae, 2021 David Kazhdan, Tamar Ziegler
openalex +3 more sources
Algebraic Combinatorics in Financial Data Analysis: Modeling Sovereign Credit Ratings for Greece and the Athens Stock Exchange General Index [PDF]
AppliedMathThis study investigates the relationship between sovereign credit rating transitions and domestic equity market performance, focusing on Greece from 2004 to 2024. Although credit ratings are central to sovereign risk assessment, their immediate influence
Georgios Angelidis, Vasilios Margaris
doaj +2 more sources
Computational Complexity in Algebraic Combinatorics [PDF]
arXiv.org, 2023 Algebraic Combinatorics originated in Algebra and Representation Theory, studying their discrete objects and integral quantities via combinatorial methods which have since developed independent and self-contained lives and brought us some beautiful ...
G. Panova
semanticscholar +1 more source
Formalising Fisher's Inequality: Formal Linear Algebraic Proof Techniques in Combinatorics [PDF]
International Conference on Interactive Theorem Proving, 2022 The formalisation of mathematics is continuing rapidly, however combinatorics continues to present challenges to formalisation efforts, such as its reliance on techniques from a wide range of other fields in mathematics. This paper presents formal linear
C. Edmonds, Lawrence Charles Paulson
semanticscholar +1 more source
Nonrepetitive colorings of lexicographic product of graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 Special issue PRIMA ...
Balázs Keszegh +2 more
doaj +1 more source
Two New Classes of Codebooks Asymptotically Achieving the Welch Bound
IEEE Access, 2021 Exponential sums over Galois rings have many applications in coding theory, cryptography and algebraic combinatorics. In this article, we employ additive characters and multiplicative characters over Galois rings to present two classes of codebooks, and ...
Shimin Sun, Li Han, Yang Yan, Yao Yao
doaj +1 more source