惯性聚合 高效追踪和阅读你感兴趣的博客、新闻、科技资讯
阅读原文 在惯性聚合中打开

推荐订阅源

Microsoft Security Blog
Microsoft Security Blog
J
Java Code Geeks
GbyAI
GbyAI
aimingoo的专栏
aimingoo的专栏
L
LangChain Blog
I
InfoQ
D
Docker
F
Fortinet All Blogs
Y
Y Combinator Blog
Martin Fowler
Martin Fowler
月光博客
月光博客
B
Blog
Engineering at Meta
Engineering at Meta
T
Tailwind CSS Blog
罗磊的独立博客
博客园_首页
G
Google Developers Blog
Stack Overflow Blog
Stack Overflow Blog
Recent Announcements
Recent Announcements
D
DataBreaches.Net
freeCodeCamp Programming Tutorials: Python, JavaScript, Git & More
B
Blog RSS Feed
IT之家
IT之家
V
V2EX

math.CO updates on arXiv.org

Complement Submodular Information Measures for Balanced and Robust Data Selection A Proof of a Conjecture on Positive and Negative Square Energies of Unicyclic Graphs Laplacian Spectrum of the Weakly Zero-Divisor Graph of a Finite Commutative Ring An identity for second Eulerian numbers via lattice-point counting $t$-tone edge coloring of graphs Constructing Maximal Bumpless Pipedreams for Double Grothendieck Polynomials Mubayi's Polynomial-Ideal Conjecture and Cover-Ideal Turán Methods Implicit Binarization via Complex Phase Dynamics in Combinatorial Optimization The limits of Schur multipliers in Pólya conversion problems for the $q$-permanent function Universality theorems for generalized splines Framing Triangulations for Arbitrary Integer Flow Polytopes On the Common Generalization of Gentle Algebras and Framed Directed Acyclic Graphs The complexity of frugal digraph homomorphisms Chaotic and periodic behavior of jeu de taquin on infinite Young tableaux Enumerating Pattern Avoiding Parking Functions Incidence toric ideals and three-point functions Unique Winning Opening Move in Three-Row Chomp Strong majority colorings of graphs A Balancing Theorem for Spanning Trees of Rectangular Grid Graphs Spectral radius and edge-disjoint connected factors of graphs New invariants for rank metric codes, with applications to the classification of rank two semifields of order 256 Flexible DP-4-coloring of planar graphs without 4-cycles and intersecting triangles Balanced intersection size distributions in projective planes List Reconstruction Problem with List Size Two Is Dimensionality a Barrier for Retrieval Models? The INIEP: Irreducible and Positive Realizations The number of Pfaffian orientations on punctured polygonally cellulated surfaces Explicit Construction of Polytopes whose Ehrhart Polynomials Realize any Given Sign Pattern Finite-state enumeration of adjacency-constrained 132-avoiding permutations AMDS and quantum AMDS Constacyclic codes of length $4p^ς$ over $\mathbb{F}_{{p}^{m}}$
From boxes to polynomials: a story of generalisation
Gypsy Akhyar, Yifan Guo, Lihexuan Yuan · 2022-03-01 · via math.CO updates on arXiv.org

Here we will embark on a journey starting with some ostensibly inauspicious boxes. Carefully stacking them in different ways yields amazing identities. From humble beginnings at the integer version: `how many steps does it take to get from row $i$ to row $j$?' to the first upgrade: the polynomial version, before finally reaching the final upgrade: the elliptic version. Each upgrade gives a more general theorem than before. Secretly, everything is controlled by the symmetric Macdonald polynomials. Setting $q = t$ in the Macdonald polynomial takes the elliptic version of the theorem to the polynomial version. Then, letting $t$ approach $1$ reduces the polynomial version to the integer version. All the beautiful theorems and ideas come merely from stacking boxes.