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combinatorics

GeneTech 知识引擎共收录 73 篇相关科研实体，横跨 16 个垂直领域。数据来自 OpenAlex、arXiv、Crossref、PubMed、Europe PMC 等公开学术源，全部可溯源到原文。

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代表性文献（按质量分排序，前 60 条）

• Families of isospectral and isoscattering quantum graphs
  2025 · 量子材料 · A concept of germ graphs and the M -function formalism are employed to construct large families of isospectral and isoscattering graphs. This approach represents a complete departure from the original approach pioneered …
• Tight bounds for antidistinguishability and circulant sets of pure quantum states
  2025 · 量子材料 · A set of pure quantum states is said to be antidistinguishable if upon sampling one at random, there exists a measurement to perfectly determine some state that was not sampled. We show that antidistinguishability of a s…
• Hidden Real Topology and Unusual Magnetoelectric Responses in Two‐Dimensional Antiferromagnets
  2024 · 量子材料 · O (ML-CrSeO) is revealed as the first material example of a 2D antiferromagnetic (AFM) real Chern insulator (RCI) with topologically protected corner states. Unlike previous RCIs, it is found that the real topology of th…
• Demonstrandum verified artifacts: nine papers in combinatorics (counterexamples, records, theorems, and Lean formalizations)
  2026 · AI Agent 生态 · Complete verification artifacts accompanying five papers by John Erlbacher: (1) a proof of the Elizalde–Luo conjecture on nonnesting pattern-avoiding multiset permutations, with a full Lean 4 formalization; (2) new recor…
• Demonstrandum verified artifacts: nine papers in combinatorics (counterexamples, records, theorems, and Lean formalizations)
  2026 · AI Agent 生态 · Complete verification artifacts accompanying five papers by John Erlbacher: (1) a proof of the Elizalde–Luo conjecture on nonnesting pattern-avoiding multiset permutations, with a full Lean 4 formalization; (2) new recor…
• A Solution of the Generalized Quantum Stein’s Lemma
  2025 · 量子计算 · We solve the generalised quantum Stein’s lemma, proving that the Stein exponent associated with entanglement testing, namely, the quantum hypothesis testing task of distinguishing between$\boldsymbol {n}$copies of an ent…
• Combining evolutionary strategies and novelty detection to go beyond the alignment limit of the Z3 3HDM
  2024 · AI 安全与对齐 · We present a novel artificial intelligence approach for beyond the Standard Model parameter space scans by augmenting an evolutionary strategy with novelty detection. Our approach leverages the power of evolutionary stra…
• Quantum Algorithm for Linear Systems of Equations
  2009 · 量子计算 · Solving linear systems of equations is a common problem that arises both on its own and as a subroutine in more complex problems: given a matrix $A$ and a vector $\stackrel{\ensuremath{\rightarrow}}{b}$, find a vector $\…
• Quantum Algorithms for the Triangle Problem
  2007 · 量子计算 · We present two new quantum algorithms that either find a triangle (a copy of $K_{3}$) in an undirected graph G on n nodes, or reject if G is triangle free. The first algorithm uses combinatorial ideas with Grover Search …
• The Quantum Supremacy Tsirelson Inequality
  2021 · 量子计算 · A leading proposal for verifying near-term quantum supremacy experiments on noisy random quantum circuits is linear cross-entropy benchmarking. For a quantum circuit C on n qubits and a sample z ∈ { 0 , 1 } n , the bench…
• On the Depth of Monotone ReLU Neural Networks and ICNNs
  2025 · AI 安全与对齐 · We study two models of ReLU neural networks: monotone networks (ReLU$^+$) and input convex neural networks (ICNN). Our focus is on expressivity, mostly in terms of depth, and we prove the following lower bounds. For the …
• Graph isomorphism and adiabatic quantum computing
  2014 · 量子计算 · In the graph isomorphism (GI) problem two $N$-vertex graphs $G$ and ${G}^{\ensuremath{'}}$ are given and the task is to determine whether there exists a permutation of the vertices of $G$ that preserves adjacency and tra…
• Topology and data
  2009 · 生物计算 · An important feature of modern science and engineering is that data of various kinds is being produced at an unprecedented rate. This is so in part because of new experimental methods, and in part because of the increase…
• Optimal Union Probability Interval Is NP-Hard
  2026 · AI 安全与对齐 · A problem dating back to Boole [Laws of Thought, Walton & Maberly,1854] is what can be computed about the probability of a finite union of events when given as input the probabilities of intersections of some of the …
• A new definition for m-Cambrian lattices
  2025 · 地外矿物 · The Cambrian lattices, introduced in (Reading, 2006), generalize the Tamari lattice to any choice of Coxeter element in any finite Coxeter group. They are further generalized to the m-Cambrian lattices (Stump, Thomas, Wi…
• The Redundancy of Full Nodes in Bitcoin: A Network-Theoretic Demonstration of Miner-Centric Propagation Topologies
  2025 · 地外矿物 · This paper formally examines the network structure of Bitcoin CORE (BTC) and Bitcoin Satoshi Vision (BSV) using complex graph theory to demonstrate that home-hosted full nodes are incapable of participating in or influen…
• Randomstrasse101: Open Problems of 2025
  2026 · AI 安全与对齐 · Randomstrasse101 is a blog dedicated to Open Problems in Mathematics, with a focus on Probability Theory, Computation, Combinatorics, Statistics, and related topics. This manuscript serves as a stable record of the Open …
• Randomstrasse101: Open Problems of 2025
  2026 · 脑科学 · Randomstrasse101 is a blog dedicated to Open Problems in Mathematics, with a focus on Probability Theory, Computation, Combinatorics, Statistics, and related topics. This manuscript serves as a stable record of the Open …
• Randomstrasse101: Open Problems of 2024
  2025 · AI 安全与对齐 · $\texttt{Randomstrasse101}$ is a blog dedicated to Open Problems in Mathematics, with a focus on Probability Theory, Computation, Combinatorics, Statistics, and related topics. This manuscript serves as a stable record o…
• Three-edge-coloring projective planar cubic graphs: A generalization of the Four Color Theorem
  2024 · 边缘智能 · We prove that every cyclically 4-edge-connected cubic graph that can be embedded in the projective plane, with the single exception of the Petersen graph, is 3-edge-colorable. In other words, the only (non-trivial) snark…
• Testing Quantum and Simulated Annealers on the Drone Delivery Packing Problem
  2024 · 低空经济 · Using drones to perform human-related tasks can play a key role in various fields, such as defense, disaster response, agriculture, healthcare, and many others. The drone delivery packing problem (DDPP) arises in the con…
• Characterization of $n$-Dimensional Toric and Burst-Error-Correcting Quantum Codes from Lattice Codes
  2024 · 量子计算 · Quantum error correction is essential for the development of any scalable quantum computer. In this work we introduce a generalization of a quantum interleaving method for combating clusters of errors in toric quantum er…
• Topologically Interlocking Blocks inside the Tetroctahedrille
  2024 · 量子计算 · A topological interlocking assembly consists of rigid blocks together with a fixed frame, such that any subset of blocks is kinematically constrained and therefore cannot be removed from the assembly. In this paper we pu…
• Quantum computing and the Jones polynomial
  2002 · 量子计算 · This paper is an exploration of relationships between the Jones polynomial and quantum computing. We discuss the structure of the Jones polynomial in relation to representations of the Temperley Lieb algebra, and give an…
• The exact quantum chromatic number of Hadamard graphs
  2024 · 量子材料 · We compute the exact value of the quantum chromatic numbers of Hadamard graphs of order $n=2^N$ for $N$ a multiple of $4$ using the upper bound derived by Avis, Hasegawa, Kikuchi, and Sasaki, as well as an application of…
• Triangular cutoff threshold for the inversion walk on tournaments and the state space of restricted inversions
  2026 · AI 安全与对齐 · Given a labelled tournament on $[n]$, \emph{inverting} a vertex subset $X$ means reversing every edge with both endpoints in $X$. Alon, Powierski, Savery, Scott, and Wilmer~\cite{AlonPowierskiSaveryScottWilmer2024} asked…
• Improved Bounds for Unavoidable Claws in Tournaments
  2026 · AI 安全与对齐 · Let $u(n)$ be the largest integer $d$ such that every $n$-vertex claw with at most $d$ branches occurs in every tournament on $n$ vertices, and let $c_{\mathrm{claw}}=\limsup_{n\to\infty}u(n)/n$. In 1998, Lu, Wang and Wo…
• Refinements of Alon-Babai-Suzuki-type intersection theorems via non-shadows and binomial support
  2026 · AI 安全与对齐 · We prove a multilevel non-shadow refinement of the Alon--Babai--Suzuki (ABS) nonuniform restricted-intersection theorem. Let $K=\{k_1,\dots,k_r\}$ and let $L$ be a set with $|L|=s$. If $\mathcal{F}\subseteq \bigcup_{k\in…
• One extra edge forces Berge pancyclicity
  2026 · 边缘智能 · We resolve a question of Bailey, Hollars, Li and Luo. For all sufficiently large $n$, let $r=\lfloor(n-1)/2\rfloor$. We prove that the edges of any Hamiltonian Berge cycle in a simple $n$-vertex $r$-uniform hypergraph, t…
• Combinatorial formulas for Macdonald polynomials by superizations
  2026 · 中医药工具 · In this paper, we derive new combinatorial formulas for symmetric Macdonald polynomials $P_λ(X;q,t)$ and non-symmetric Macdonald polynomials $E_γ(X;q,t)$, in terms of several new statistics and the major index, for a par…
• The Specter (and Spectra) of Miner Extractable Value
  2023 · 地外矿物 · Miner extractable value (MEV) refers to any excess value that a transaction validator can realize by manipulating the ordering of transactions. In this work, we introduce a simple theoretical definition of the 'cost of M…
• On functions computed on trees
  2019 · 生物计算 · Any function can be constructed using a hierarchy of simpler functions through compositions. Such a hierarchy can be characterized by a binary rooted tree. Each node of this tree is associated with a function which takes…
• A framework for cost-constrained genome rearrangement under Double Cut and Join
  2018 · 生命科学 · The study of genome rearrangement has many flavours, but they all are somehow tied to edit distances on variations of a multi-graph called the breakpoint graph. We study a weighted 2-break distance on Eulerian 2-edge-col…
• Computing error bounds for asymptotic expansions of regular P-recursive sequences
  2022 · 生物计算 · Over the last several decades, improvements in the fields of analytic combinatorics and computer algebra have made determining the asymptotic behaviour of sequences satisfying linear recurrence relations with polynomial …
• A notion of twins
  2023 · 数字孪生 · Given a combinatorial structure, a ``twin'' is a pair of disjoint substructures which are isomorphic (or look the same in some sense). In recent years, there have been many problems about finding large twins in various c…
• The Harer-Zagier and Jackson formulas and new results for one-face bipartite maps
  2023 · 中医药工具 · The study of bipartite maps (or Grothendieck's dessins d'enfants) is closely connected with geometry, mathematical physics and free probability. Here we study these objects from their permutation factorization formulatio…
• Open problems of the 32nd Workshop on Cycles and Colourings
  2024 · AI 安全与对齐 · Since its beginnings, every Cycles and Colourings workshop holds one or two open problem sessions; this document contains the problems (together with notes regarding the current state of the art and related bibliography)…
• Complex Golay Pairs up to Length 28: A Search via Computer Algebra and Programmatic SAT
  2019 · 生物计算 · We use techniques from the fields of computer algebra and satisfiability checking to develop a new algorithm to search for complex Golay pairs. We implement this algorithm and use it to perform a complete search for comp…
• Applying Computer Algebra Systems with SAT Solvers to the Williamson Conjecture
  2018 · 生物计算 · We employ tools from the fields of symbolic computation and satisfiability checking---namely, computer algebra systems and SAT solvers---to study the Williamson conjecture from combinatorial design theory and increase th…
• Spectral Alignment of Graphs
  2016 · AI 安全与对齐 · Graph alignment refers to the problem of finding a bijective mapping across vertices of two graphs such that, if two nodes are connected in the first graph, their images are connected in the second graph. This problem ar…
• Generalized Ramsey numbers through adiabatic quantum optimization
  2016 · 量子计算 · Ramsey theory is an active research area in combinatorics whose central theme is the emergence of order in large disordered structures, with Ramsey numbers marking the threshold at which this order first appears. For gen…
• Weak Integer Additive Set-Indexed Graphs: A Creative Review
  2014 · AI 安全与对齐 · For a non-empty ground set $X$, finite or infinite, the {\em set-valuation} or {\em set-labeling} of a given graph $G$ is an injective function $f:V(G) \to \mathcal{P}(X)$, where $\mathcal{P}(X)$ is the power set of the …
• Encoding binary neural codes in networks of threshold-linear neurons
  2012 · 仿生智能 · Networks of neurons in the brain encode preferred patterns of neural activity via their synaptic connections. Despite receiving considerable attention, the precise relationship between network connectivity and encoded pa…
• Encoding binary neural codes in networks of threshold-linear neurons
  2012 · 脑科学 · Networks of neurons in the brain encode preferred patterns of neural activity via their synaptic connections. Despite receiving considerable attention, the precise relationship between network connectivity and encoded pa…
• A combinatorial description of the affine Gindikin-Karpelevich formula of type A_n^(1)
  2012 · 中医药工具 · The classical Gindikin-Karpelevich formula appears in Langlands' calculation of the constant terms of Eisenstein series on reductive groups and in Macdonald's work on p-adic groups and affine Hecke algebras. The formula …
• Parametric Alignment of Drosophila Genomes
  2005 · AI 安全与对齐 · The classic algorithms of Needleman--Wunsch and Smith--Waterman find a maximum a posteriori probability alignment for a pair hidden Markov model (PHMM). In order to process large genomes that have undergone complex genom…
• Parametric Alignment of Drosophila Genomes
  2005 · 生命科学 · The classic algorithms of Needleman--Wunsch and Smith--Waterman find a maximum a posteriori probability alignment for a pair hidden Markov model (PHMM). In order to process large genomes that have undergone complex genom…
• A Linear Lower Bound for Dominating Sets in $k$-Majority Tournaments
  2026 · AI 安全与对齐 · A $k$-majority tournament on a finite vertex set is defined by $2k-1$ linear orders, with $u\to v$ when $u$ lies above $v$ in at least $k$ of the orders. Let $F(k)$ be the maximum, over all $k$-majority tournaments, of t…
• A formula for the number of up-down words
  2025 · 中医药工具 · A word $w_1w_2\cdots w_n$ is said to be up-down if $w_1 < w_2 >w_3 \cdots$. Carlitz and Scoville found the generating function for the number of up-down words over an alphabet of size $k$. Using properties of the C…
• The Up Topology for Mirrored Topological Posets
  2020 · 量子计算 · For a discrete poset $\mathcal X$, McCord proved that the natural map $|{\mathcal X}|\to {\mathcal X}$, from the order complex to the poset with the Up topology, is a weak homotopy equivalence. Much later, uZivaljević de…
• Hook formulas for skew shapes IV. Increasing tableaux and factorial Grothendieck polynomials
  2021 · 中医药工具 · We present a new family of hook-length formulas for the number of standard increasing tableaux which arise in the study of factorial Grothendieck polynomials. In the case of straight shapes our formulas generalize the cl…
• Perfectly Clustering Words and Iterated Palindromes over a Ternary Alphabet
  2024 · 地外矿物 · Recently, a new characterization of Lyndon words that are also perfectly clustering was proposed by Lapointe and Reutenauer (2024). A word over a ternary alphabet {a,b,c} is called perfectly clustering Lyndon if and only…
• Ramanujan Graphs and Interlacing Families
  2024 · 地外矿物 · This survey accompanies a lecture on the paper ``Interlacing Families I: Bipartite Ramanujan Graphs of All Degrees'' by A. Marcus, D. Spielman, and N. Srivastava at the 2024 International Congress of Basic Science (ICBS)…
• An extension of the cogrowth formula to arbitrary subsets of the tree
  2024 · 中医药工具 · What is the probability that a random walk in the free group ends in a proper power? Or in a primitive element? We present a formula that computes the exponential decay rate of the probability that a random walk on a reg…
• Construction of storage codes of rates approaching one on triangle-free graphs
  2023 · 碳中和与 CCUS · Consider an assignment of bits to the vertices of a connected graph $Γ(V, E)$ with the property that the value of each vertex is a function of the values of its neighbors. A collection of such assignments is called a sto…
• Effective Coefficient Asymptotics of Multivariate Rational Functions via Semi-Numerical Algorithms for Polynomial Systems
  2019 · 生物计算 · The coefficient sequences of multivariate rational functions appear in many areas of combinatorics. Their diagonal coefficient sequences enjoy nice arithmetic and asymptotic properties, and the field of analytic combinat…
• Product formulas on posets, Wick products, and a correction for the $q$-Poisson process
  2017 · 中医药工具 · We give an example showing that the product and linearization formulas for the Wick product versions of the $q$-Charlier polynomials in (Anshelevich 2004) are incorrect. Next, we observe that the relation between monomia…
• On twin and anti-twin words in the support of the free Lie algebra
  2010 · 数字孪生 · Let $L_{K}(A)$ be the free Lie algebra on a finite alphabet $A$ over a commutative ring $K$ with unity. For a word $u$ in the free monoid $A^{*}$ let $\tilde{u}$ denote its reversal. Two words in $A^{*}$ are called twin …
• On the computation of classical, boolean and free cumulants
  2008 · 生物计算 · This paper introduces a simple and computationally efficient algorithm for conversion formulae between moments and cumulants. The algorithm provides just one formula for classical, boolean and free cumulants. This is rea…
• Hook formulas for skew shapes III. Multivariate and product formulas
  2017 · 中医药工具 · We give new product formulas for the number of standard Young tableaux of certain skew shapes and for the principal evaluation of the certain Schubert polynomials. These are proved by utilizing symmetries for evaluations…

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