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On Turán-type problems and the abstract chromatic number
In 2020, Coregliano and Razborov introduced a general framework to study limits of combinatorial objects, using logic and model theory. They introduced the abstract chromatic number and proved/reproved multiple Erd\H{o}s-Stone-S ... Read More >
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Combinatorial optimization of the coefficient of determination
Robust correlation analysis is among the most critical challenges in statistics. Herein, we develop an efficient algorithm for selecting the $k$- subset of $n$ points in the plane with the highest coefficient of determination $\ ... Read More >
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Metric Dimension of Villarceau Grids
The metric dimension of a graph measures how uniquely vertices may be identified using a set of landmark vertices. This concept is frequently used in the study of network architecture, location-based problems and communication. ... Read More >
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Twisted fusion products and quantum twisted Q-systems
We obtain a complete characterization of the space of matrix elements dual to the graded multiplicity space arising from fusion products of Kirillov-Reshetikhin modules over special twisted current algebras defined by Kus and Ve ... Read More >
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Canonical Ramsey numbers of sparse graphs
The canonical Ramsey theorem of Erd\H{o}s and Rado implies that for any graph $H$, any edge-coloring (with an arbitrary number of colors) of a sufficiently large complete graph $K_N$ contains a monochromatic, lexicographic, or r ... Read More >
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On the total number of ones associated with cranks of partitions modulo 11
In 2021, Andrews mentioned that George Beck introduced partition statistics $M_w(r,m,n)$, which denote the total number of ones in the partition of $n$ with crank congruent to $r$ modulo $m$. Recently, a number of congruences an ... Read More >
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A study of nil Hecke algebras via Hopf algebroid theory
Hopf algebroids are generalizations of Hopf algebras to less commutative settings. We show how the comultiplication defined by Kostant and Kumar turns the affine nil Hecke algebra associated to a Coxeter system a into Hopf algeb ... Read More >
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Parking functions with a fixed set of lucky cars
In a parking function, a lucky car is a car that parks in its preferred parking spot and the parking outcome is the permutation encoding the order in which the cars park on the street. We give a characterization for the set of p ... Read More >
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Double orthodontia formulas and Lascoux positivity
We give a new formula for double Grothendieck polynomials based on Magyar's orthodontia algorithm for diagrams. Our formula implies a similar formula for double Schubert polynomials $\mathfrak S_w(\mathbf x;\mathbf y)$. We also ... Read More >
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Binary geometries from pellytopes
Binary geometries have recently been introduced in particle physics in connection with stringy integrals. In this work, we study a class of simple polytopes, called \emph{pellytopes}, whose number of vertices are given by Pell's ... Read More >