Related papers: Graded posets inverse zeta matrix formula
In this dissertation, we explore the structure of inversion graphs of permutations--a class of graphs that naturally arises by representing each permutation as a graph, where vertices correspond to entries and edges encode inversions.…
Given polynomials a(z) of degree m and b(z) of degree n, we represent the inverse to the Sylvester resultant matrix of a(z) and b(z), if this inverse exists, as a canonical sum of m+n dyadic matrices each of which is a rational function of…
In this paper, we consider ordered set partitions obtained by imposing conditions on the size of the lists, and such that the first $r$ elements are in distinct blocks, respectively. We introduce a generalization of the Lah numbers. For…
In this paper, we compute the posets of wide subcategories and ICE-closed subcategories from the lattice of torsion classes in an abelian length category in a purely lattice-theoretical way, by using the kappa map in a completely…
We derive new infinite series involving Fibonacci numbers and Riemann zeta numbers. The calculations are facilitated by evaluating linear combinations of polygamma functions of the same order at certain arguments.
A class of bilinear permutation polynomials over a finite field of characteristic 2 was constructed in a recursive manner recently which involved some other constructions as special cases. We determine the compositional inverses of them…
For a one-parameter family of lower triangular matrices with entries involving continuous $q$-ultraspherical polynomials we give an explicit lower triangular inverse matrix, with entries involving again continuous $q$-ultraspherical…
In this paper, we show that any finite simplicial complex is homeomorphic to the inverse limit of a sequence of finite posets, which is an extension of Claders result.
In this paper, we present an algorithm that enumerates a certain class of signed permutations, referred to as grid signed permutation classes. In the case of permutations, the corresponding grid classes are of interest because they are…
It is well-understood that the robustness of mechanical and robotic control systems depends critically on minimizing sensitivity to arbitrary application-specific details whenever possible. For example, if a system is defined and performs…
We introduce certain special polynomials in an arbitrary number of indeterminates over a finite field. These polynomials generalize the special polynomials associated to the Goss zeta function and Goss-Dirichlet $L$-functions over the ring…
Ap\'{e}ry-type (inverse) binomial series have appeared prominently in the calculations of Feynman integrals in recent years. In our previous work, we showed that a few large classes of the non-alternating Ap\'ery-type (inverse) central…
Nested sums containing binomial coefficients occur in the computation of massive operator matrix elements. Their associated iterated integrals lead to alphabets including radicals, for which we determined a suitable basis. We discuss…
New formulas for approximation of zeta-constants were derived on the basis of a number-theoretic approach constructed for the irrationality proof of certain classical constants. Using these formulas it's possible to approximate certain…
Three-graded root systems can be arranged into nested sequences. One exceptional sequence provides a natural means to recover some structures and symmetries familiar in the context of particle physics.
In the last decade, the order polytope of the zigzag poset has been thoroughly studied. A related poset, called \emph{crown poset}, obtained by adding an extra relation between the endpoints of an even zigzag poset, is not so well…
For a composition $I$ whose first part exceeds 1, we can define the multiple $t$-value $t(I)$ as the sum of all the terms in the series for the multiple zeta value $\zeta(I)$ whose denominators are odd. In this paper we show that if $I$ is…
In this paper, we obtain a restricted decomposition formula for interpolated multiple zeta values using t-stuffle product. We then derive a recursive formula of t-stuffle product, which also provides a route to the same formula. In both…
The core-EP and BT inverses for rectangular matrices were studied recently in the literature. The main aim of this paper is to unify both concepts by means of a new kind of generalized inverse called $W$-weighted $q$-BT inverse. We analyze…
The magnitude of finite categories is a generalization of the Euler characteristic. It is defined using the coarse incidence algebra of rational-valued functions on the given finite category, and a distinguished element in this algebra: the…