Advances in Applied Mathematics最新文献

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IF 1.3 3区数学 Q3 MATHEMATICS, APPLIED

Advances in Applied Mathematics

Pub Date : 2026-01-01

引用次数: 0

IF 1.3 3区数学 Q3 MATHEMATICS, APPLIED

Advances in Applied Mathematics

Pub Date : 2026-01-01

引用次数: 0

IF 1.3 3区数学 Q3 MATHEMATICS, APPLIED

Advances in Applied Mathematics

Pub Date : 2026-01-01

引用次数: 0

IF 1.3 3区数学 Q3 MATHEMATICS, APPLIED

Advances in Applied Mathematics

Pub Date : 2026-01-01

引用次数: 0

Exact multi-parameter persistent homology of time-series data: Fast and variable topological inferences 时间序列数据的精确多参数持久同调：快速和可变的拓扑推断

IF 1.3 3区数学 Q3 MATHEMATICS, APPLIED

Advances in Applied Mathematics

Pub Date : 2025-12-23 DOI: 10.1016/j.aam.2025.103023

Keunsu Kim , Jae-Hun Jung

We propose the Exact Multi-Parameter Persistent Homology (EMPH) method for the topological analysis of time-series data based on the Liouville torus. Assuming, as in Takens' embedding, that a time-series represents observations of an underlying dynamical system, we model the system as a Hamiltonian system of uncoupled one-dimensional harmonic oscillators. Under this setting, the Liouville torus arises naturally as a dynamical object, and the persistent homology of the Vietoris–Rips complex built on this torus can be interpreted through Fourier analysis. EMPH constructs a multi-parameter filtration framework using Fourier decomposition and provides a closed-form expression for the fibered barcode, an invariant obtained by restricting multi-parameter persistent homology along a specific ray. This formulation establishes a direct correspondence between the choice of a ray and the weighting of Fourier modes, enabling variable topological inferences by exploring different rays in the filtration space. Compared with conventional sliding window based analysis of time-series data, which is computationally expensive, EMPH yields exact barcode formulas with the symmetry of the Liouville torus, achieving much lower computational cost while maintaining comparable or superior accuracy. Thus, EMPH offers both computational efficiency and interpretive flexibility, bridging Fourier analysis and multi-parameter persistent homology in time-series data analysis.

提出了基于Liouville环面的时间序列数据拓扑分析的精确多参数持久同调（EMPH）方法。假设，在Takens的嵌入中，一个时间序列代表一个潜在的动力系统的观测，我们将该系统建模为一个不耦合的一维谐振子的哈密顿系统。在这种情况下，刘维尔环面作为一个动态物体自然产生，而建立在这个环面上的Vietoris-Rips复合体的持续同构性可以通过傅里叶分析来解释。EMPH利用傅里叶分解构造了一个多参数过滤框架，并为光纤条形码提供了一个封闭形式的表达式，该表达式是通过限制沿特定射线的多参数持久同源性而获得的不变量。该公式在射线的选择和傅里叶模式的权重之间建立了直接对应关系，通过探索过滤空间中的不同射线来实现可变拓扑推断。与传统的基于滑动窗口的时间序列数据分析相比，EMPH产生精确的条形码公式，具有刘维尔环面的对称性，计算成本低得多，同时保持相当或更高的精度。因此，EMPH提供了计算效率和解释灵活性，在时间序列数据分析中架起了傅里叶分析和多参数持久同源性的桥梁。

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引用次数: 0

Macdonald polynomials at t = 0 through twisted multiline queues 扭曲多行队列在t = 0处的麦克唐纳多项式

IF 1.3 3区数学 Q3 MATHEMATICS, APPLIED

Advances in Applied Mathematics

Pub Date : 2025-12-15 DOI: 10.1016/j.aam.2025.103020

Olya Mandelshtam, Jerónimo Valencia-Porras

Multiline queues are versatile combinatorial objects that play a key role in understanding the remarkable connection between the asymmetric simple exclusion process (ASEP) on a circle and Macdonald polynomials. Specializing the results of Corteel–Mandelshtam–Williams (2018) to the

t = 0

case yields a formula for the q-Whittaker polynomials through the Ferrari–Martin (2007) algorithm with a major index (maj) statistic. In this paper, we reinterpret the maj statistic as a charge statistic on reading words, thereby bypassing the Ferrari–Martin algorithm to obtain an elegant formula for the q-Whittaker polynomials. Our methods naturally extend to the case of bosonic multiline queues, with which we obtain analogous results for the modified Hall–Littlewood polynomials using a cocharge statistic on reading words.

Twisted multiline queues (TMLQs) are obtained from the action of the symmetric group on the rows of a multiline queue. The Ferrari–Martin algorithm was extended to TMLQs by Arita–Ayyer–Mallick–Prolhac (2011), and Aas–Grinberg–Scrimshaw (2020) showed it is preserved under this action. We extend these results by defining a maj statistic on TMLQs that is also preserved under this action. This yields a novel family of formulas, indexed by compositions, for the q-Whittaker polynomials. Additionally, we define a procedure on both TMLQs and bosonic multiline queues that we call collapsing, which can be realized via the Kashiwara (crystal) operators on type-A Kirillov–Reshetikhin crystals. As an application, we naturally recover the Lascoux–Schützenberger charge formula for the q-Whittaker and modified Hall–Littlewood polynomials, and the classical and dual Cauchy identities for Schur functions.

多行队列是一种多用途的组合对象，它在理解圆上的非对称简单不相容过程（ASEP）与麦克唐纳多项式之间的显著联系方面起着关键作用。将Corteel-Mandelshtam-Williams（2018）的结果专一化到t=0的情况下，通过带有主要指数（maj）统计量的Ferrari-Martin（2007）算法得出q-Whittaker多项式的公式。在本文中，我们将主要统计量重新解释为阅读词的电荷统计量，从而绕过法拉利-马丁算法，获得q-Whittaker多项式的优雅公式。我们的方法自然地扩展到玻色子多行队列的情况下，我们使用阅读单词的共电荷统计量获得了修改的Hall-Littlewood多项式的类似结果。扭曲多行队列（tmlq）是由对称组对多行队列的行进行操作而获得的。Ferrari-Martin算法被arita - ayer - mallick - prolhac（2011）扩展到tmlq， Aas-Grinberg-Scrimshaw（2020）表明在这种作用下它是保持不变的。我们通过定义tmlq的主要统计数据来扩展这些结果，该统计数据也在此操作下保留。这为q-Whittaker多项式提供了一组新的公式，以组合为索引。此外，我们在tmlq和玻色子多行队列上定义了一个我们称之为坍缩的过程，这可以通过a型Kirillov-Reshetikhin晶体上的Kashiwara（晶体）算子实现。作为应用，我们自然地恢复了q-Whittaker多项式和修正Hall-Littlewood多项式的lascoux - sch岑伯格电荷公式，以及Schur函数的经典和对偶Cauchy恒等式。

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引用次数: 0

Spectral conditions for k-extendability and k-factors of bipartite graphs 二部图的k可拓性和k因子的谱条件

IF 1.3 3区数学 Q3 MATHEMATICS, APPLIED

Advances in Applied Mathematics

Pub Date : 2025-12-11 DOI: 10.1016/j.aam.2025.103019

Dandan Fan , Huiqiu Lin

Let G be a connected graph. If G contains a matching of size k, and every matching of size k is contained in a perfect matching of G, then G is said to be k-extendable. A k-regular spanning subgraph of G is called a k-factor. In this paper, we provide spectral conditions for a (balanced bipartite) graph with minimum degree δ to be k-extendable, and for the existence of a k-factor in a balanced bipartite graph, respectively. Our results generalize some previous results on perfect matchings of graphs, and extend the results in [12] and [27] to k-extendable graphs. Furthermore, our results generalize the result of Lu, Liu and Tian [24] to general regular factors. Additionally, using the equivalence of k edge-disjoint perfect matchings and k-factors in balanced bipartite graphs, our results can derive a spectral condition for the existence of k edge-disjoint perfect matchings in balanced bipartite graphs.

设G是连通图。如果G包含大小为k的匹配，并且每个大小为k的匹配都包含在G的完美匹配中，则称G是k可扩展的。G的k正则生成子图称为k因子。本文分别给出了最小度为δ的平衡二部图可k扩展的谱条件，以及平衡二部图中存在k因子的谱条件。我们的结果推广了先前关于图的完美匹配的一些结果，并将[12]和[27]中的结果推广到k-可扩展图。此外，我们的结果将Lu， Liu和Tian b[24]的结果推广到一般规则因子。此外，利用平衡二部图中k个边不相交完美匹配与k个因子的等价性，我们的结果可以导出平衡二部图中k个边不相交完美匹配存在的谱条件。

引用次数: 0

Gapfree graphs and powers of edge ideals with linear quotients 带线性商的无间隙图和边理想的幂

IF 1.3 3区数学 Q3 MATHEMATICS, APPLIED

Advances in Applied Mathematics

Pub Date : 2025-12-05 DOI: 10.1016/j.aam.2025.103004

Nursel Erey , Sara Faridi , Tài Huy Hà , Takayuki Hibi , Selvi Kara , Susan Morey

Let

I (G)

be the edge ideal of a gapfree graph G. An open conjecture of Nevo and Peeva states that

I {(G)}^{q}

has a linear resolution for

q ≫ 0

. We present a promising approach to this challenging conjecture by investigating the stronger property of linear quotients. Specifically, we make the conjecture that if

I {(G)}^{q}

has linear quotients for some integer

q \geq 1

, then

I {(G)}^{s}

has linear quotients for all

s \geq q

. We give a partial solution to this conjecture by considering a special order of the generators of

I {(G)}^{q}

. It is known that if G does not contain a cricket, a diamond, or a cycle

C_{4}

of length 4, then

I {(G)}^{q}

has a linear resolution for

q \geq 2

. We construct a family of gapfree graphs G containing a cricket, a diamond, a

C_{4}

together with a cycle

C_{5}

of length 5 as induced subgraphs of G for which

I {(G)}^{q}

has linear quotients for

q \geq 2

设I(G)为无间隙图G的边理想。Nevo和Peeva的一个开放猜想表明I(G)q在q≠0时具有线性分辨率。我们通过研究线性商的更强性质，提出了一个有希望的方法来解决这个具有挑战性的猜想。具体地说，我们假设如果I(G)q对于某个整数q≥1有线性商，那么I(G)s对于所有s≥q都有线性商。通过考虑I(G)q的生成子的特殊阶，给出了这个猜想的部分解。已知，如果G不包含长度为4的蟋蟀、菱形或循环C4，则I(G)q具有q≥2的线性分辨率。我们构造了一组无间隙图G，其中包含一个蟋蟀，一个菱形，一个C4和一个长度为5的循环C5作为G的诱导子图，其中I(G)q具有q≥2的线性商。

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引用次数: 0

Decomposing conditional independence ideals with hidden variables 带隐变量的条件独立理想分解

IF 1.3 3区数学 Q3 MATHEMATICS, APPLIED

Advances in Applied Mathematics

Pub Date : 2025-12-04 DOI: 10.1016/j.aam.2025.103003

Yulia Alexandr , Kristen Dawson , Hannah Friedman , Fatemeh Mohammadi , Pardis Semnani , Teresa Yu

We study a family of determinantal ideals whose decompositions encode the structural zeros in conditional independence models with hidden variables. We provide explicit decompositions of these ideals and, for certain subclasses of models, we show that this is a decomposition into radical ideals by displaying Gröbner bases for the components. We identify conditions under which the components are prime, and establish formulas for the dimensions of these prime ideals. We show that the components in the decomposition can be grouped into equivalence classes defined by their combinatorial structure, and we derive a closed formula for the number of such classes.

我们研究了一类决定理想，它们的分解编码了具有隐变量的条件独立模型中的结构零。我们提供了这些理想的显式分解，并且，对于模型的某些子类，我们通过显示组件的Gröbner基来表明这是对基本理想的分解。我们确定了成分为素数的条件，并建立了这些素数理想的维数公式。我们证明了分解中的分量可以被归为由它们的组合结构所定义的等价类，并导出了等价类数目的封闭公式。

引用次数: 0

Degeneration in discriminantal arrangements 歧视性安排的退化

IF 1.3 3区数学 Q3 MATHEMATICS, APPLIED

Advances in Applied Mathematics

Pub Date : 2025-11-24 DOI: 10.1016/j.aam.2025.103001

Takuya Saito

Discriminantal arrangements are hyperplane arrangements that are generalization of braid arrangements. They are constructed from given hyperplane arrangements, but their combinatorics are not invariant under combinatorial equivalence. However, it is known that the combinatorics of the discriminantal arrangements are constant on a Zariski open set of the space of hyperplane arrangements. In the present paper, we introduce

(T, r)

-singularity varieties in the space of hyperplane arrangements to classify discriminantal arrangements and show that the Zariski open set is the complement of

(T, r)

-singularity varieties. We study their basic properties and operations and provide examples, including infinite families of

(T, r)

-singularity varieties. In particular, the operation that we call degeneration is a powerful tool for constructing

(T, r)

-singularity varieties. As an application, we provide a list of

(T, r)

-singularity varieties for spaces of small line arrangements.

判别排列是超平面排列，是辫状排列的推广。它们是由给定的超平面排列构造而成，但在组合等价条件下，它们的组合不是不变的。然而，在超平面排列空间的Zariski开集上，判别排列的组合是常数。本文在超平面排列空间中引入(T,r)-奇异变异体来对判别式排列进行分类，并证明Zariski开集是(T,r)-奇异变异体的补集。我们研究了它们的基本性质和运算，并举例说明了(T,r)-奇点的无穷族。特别地，我们称之为退化的操作是构造(T,r)-奇点变体的有力工具。作为一种应用，我们给出了小线排列空间的(T,r)-奇点变体的列表。

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引用次数: 0

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