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We derive new explicit results for the Hilbert series of N=1 supersymmetric QCD with U(N_c) and SU(N_c) color symmetry. We use two methods which have previously been applied to similar computational problems in the analysis of decay of…
We study the problem of designing multiwinner voting rules that are candidate monotone and proportional. We show that the set of committees satisfying the proportionality axiom of proportionality for solid coalitions is candidate monotone.…
We present a new solution of the asymmetric two-matrix model in the large $N$ limit which only involves a saddle point analysis. The model can be interpreted as Ising in the presence of a magnetic field, on random dynamical lattices with…
Suppose that $\mathbb{F}_p$ is coloured with $r$ colours. Then there is some colour class containing at least $c_r p^2$ quadruples of the form $(x, y , x + y, xy)$.
A combinatorial study discloses two surjective morphisms between generalized shuffle algebras and algebras generated by the colored Hurwitz polyz\^etas. The combinatorial aspects of the products and co-products involved in these algebras…
In his recent work, Andrews revisited two-color partitions with certain restrictions on the differences between consecutive parts, and he established three theorems linking these two-color partitions with more familiar kinds of partitions.…
A color octet isodoublet can have esoteric origins and it complies with minimal flavour violation. In this study, we take a scenario where the well known Type-X Two-Higgs doublet model is augmented with a color octet isodoublet. We shed…
We study the joint asymptotics of forward and backward processes of numbers of non-empty urns in an infinite urn scheme. The probabilities of balls hitting the urns are assumed to satisfy the conditions of regular decrease. We prove weak…
In this expository note, we discuss a ``balls-and-urns'' probability puzzle posed by Daniel Litt.
We transform the two-matrix model, studied by P.Di Francesco and al., into a normal one-matrix model by identifying a ``formal'' integral used by these authors as a proper integral. We show also, using their method, that the results…
Concentration results and probabilistic analysis for combinatorial problems like the TSP, MWST, graph coloring have received much attention, but generally, for i.i.d. samples (i.i.d. points in the unit square for the TSP, for example).…
In this paper, we propose a novel multi-color balance adjustment for color constancy. The proposed method, called "n-color balancing," allows us not only to perfectly correct n target colors on the basis of corresponding ground truth colors…
In clinical studies with paired organs, binary outcomes often exhibit intra-subject correlation and may include a mixture of unilateral and bilateral observations. Under Donner's constant correlation model, we develop three likelihood-based…
It is consistent that ZF+DC holds, the hypergraph of rectangles on a given Euclidean space has countable chromatic number, while the hypergraph of equilateral triangles in two-dimensional Euclidean space does not.
Weighted cone-volume functionals are introduced for the convex polytopes in $\mathbb{R}^n$. For these functionals, geometric inequalities are proved and the equality conditions are characterized. A variety of corollaries are derived,…
We refine Schmidt's problem and a partition identity related to 2-color partitions which we will refer to as Uncu-Andrews-Paule theorem. We will approach the problem using Boulet-Stanley weights and a formula on Rogers-Szeg\H{o} polynomials…
In this paper, we propose a novel white balance adjustment, called "spatially varying white balancing," for single, mixed, and non-uniform illuminants. By using n diagonal matrices along with a weight, the proposed method can reduce…
Split-plot designs find wide applicability in multifactor experiments with randomization restrictions. Practical considerations often warrant the use of unbalanced designs. This paper investigates randomization based causal inference in…
Colour symmetries with ten colours are presented for different tilings. In many cases, the existence of these colourings were predicted by group theoretical methods. Only in a few cases explicit constructions were known, sometimes using…
In the modified Bonn quark model in which quark-pairing and particle-hole interactions are included, color-singlet states are examined in addition to the color-neutral quark-triplet state by a method of boson realization. The region which…