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Related papers: Note on symmetric BCJ numerator

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In the present paper, we give harmonic weight enumerators and Jacobi polynomials for the first-order Reed--Muller codes and the extended Hamming codes. As a corollary, we show the nonexistence of combinatorial $4$-designs in these codes.

Combinatorics · Mathematics 2024-01-03 Tsuyoshi Miezaki , Akihiro Munemasa

In this paper, we consider solving a class of nonconvex and nonsmooth problems frequently appearing in signal processing and machine learning research. The traditional alternating direction method of multipliers encounters troubles in both…

Numerical Analysis · Computer Science 2018-10-17 Tao Sun , Hao Jiang , Lizhi Cheng , Wei Zhu

In 1995 Stanley conjectured that the chromatic symmetric functions of the graphs $P_{d,2}$, which we call triangular ladders, were $e$-positive. In this paper we confirm this conjecture, which is also an unsolved case of the celebrated…

Combinatorics · Mathematics 2019-07-02 Samantha Dahlberg

We propose and recursively prove polynomial identities which imply Capparelli's partition theorems. We also find perfect companions to the results of Andrews, and Alladi, Andrews and Gordon involving $q$-trinomial coefficients. We follow…

Number Theory · Mathematics 2019-02-18 Alexander Berkovich , Ali K. Uncu

In this note we introduce a new technique to answer an issue posed in [7] concerning geometric properties of the set of non-surjective linear operators. We also extend and improve a related result from the same paper.

Functional Analysis · Mathematics 2020-09-08 Diogo Diniz , Anselmo Raposo

We discuss the renormalisation of mixed 3-point functions involving tensorial and scalar operators in conformal field theories of general dimension. In previous work we analysed correlators of either purely scalar or purely tensorial…

High Energy Physics - Theory · Physics 2018-12-12 Adam Bzowski , Paul McFadden , Kostas Skenderis

In geometry processing, numerical optimization methods often involve solving sparse linear systems of equations. These linear systems have a structure that strongly resembles to adjacency graphs of the underlying mesh. We observe how…

Numerical Analysis · Computer Science 2015-10-06 Nicolas Ray , Sokolov Dmitry

For every linear binary code $C$, we construct a geometric triangular configuration $\Delta$ so that the weight enumerator of $C$ is obtained by a simple formula from the weight enumerator of the cycle space of $\Delta$. The triangular…

Combinatorics · Mathematics 2010-08-23 Pavel Rytíř

We provide a natural BMO-criterion for the $L_2$-boundedness of Calder\'on-Zygmund operators with operator-valued kernels satisfying a symmetric property. Our arguments involve both classical and quantum probability theory. In the appendix,…

Classical Analysis and ODEs · Mathematics 2019-07-26 Guixiang Hong , Honghai Liu , Tao Mei

This article presents new enumerative results related to symmetric planar maps. In the first part a new way of enumerating rooted simple quadrangulations and rooted simple triangulations is presented, based on the description of two…

Combinatorics · Mathematics 2012-09-17 Marie Albenque , Eric Fusy , Dominique Poulalhon

This article presents a methodology that automatically derives a combinatorial specification for a permutation class C, given its basis B of excluded patterns and the set of simple permutations in C, when these sets are both finite. This is…

Combinatorics · Mathematics 2016-11-01 Frédérique Bassino , Mathilde Bouvel , Adeline Pierrot , Carine Pivoteau , Dominique Rossin

We exhibit generically nonreduced components of the Hilbert scheme of at least $21$ points on a smooth variety of dimension at least four. The result was announced in~[Jelisiejew__open_problems] and answers a question~[Problem~3.8, AIMPL].…

Algebraic Geometry · Mathematics 2024-07-01 Joachim Jelisiejew

The present paper is devoted to the study of the well-posedness of a type of BSDEs with triangularly quadratic generators. This work is motivated by the recent results obtained by Hu and Tang [14] and Xing and \v{Z}itkovi\'{c} [28]. By the…

Probability · Mathematics 2019-04-29 Peng Luo

We obtain a three-parameter $q$-series identity that generalizes two results of Chan and Mao. By specializing our identity, we derive new results of combinatorial significance in connection with $N(r, s, m, n)$, a function counting certain…

Combinatorics · Mathematics 2022-01-19 Atul Dixit , Ankush Goswami

We prove that the well-known condition of being a balanced labeling can be characterized in terms of the sliding algorithm on tower diagrams. The characterization involves a generalization of authors' Rothification algorithm. Using the…

Combinatorics · Mathematics 2016-08-11 Olcay Coşkun , Müge Taşkın

The aim of this study is to show that harmonic geometric polynomials can be represented in terms of geometric polynomials. This problem was first considered by Keller [14]; however, the corresponding coefficients were not fully determined.…

Number Theory · Mathematics 2025-12-09 Pınar Akkanat , Levent Kargın

In this note, we provide bijective proofs of some identities involving the Bell number, as previously requested. Our arguments may be extended to yield a generalization in terms of complete Bell polynomials. We also provide a further…

Combinatorics · Mathematics 2014-01-28 Mark Shattuck

This paper aims to characterize rank-one arithmetic and locally symmetric metrics in the coarsely geometric setting using coarse-geometric commensurators. We provide a positive answer in general under the Hilbert-Smith conjecture and…

Geometric Topology · Mathematics 2024-12-11 Yanlong Hao

We study some properties convex functions fulfill. Among the conclusions we obtain from such result, we are able to prove some nontrivial inequalities among real numbers, and we give an improvement of the reverse triangle inequality in the…

We have developed an efficient tabulation scheme to evaluate $6j$ symbol for atomic calculations. The scheme is appropriate for coupled-cluster based calculations. In particular, for perturbed coupled-clusters calculations, which has…

Atomic Physics · Physics 2008-05-20 K. V. P. Latha , Dilip Angom , B. P. Das
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