Related papers: Identities for Schur-type determinants and pfaffia…
We study some properties of restricted and associated Fubini numbers. In particular, they have the natural extensions of the original Fubini numbers in the sense of determinants. We also introduce modified Bernoulli and Cauchy numbers and…
We show that, for a certain class of partitions and an even number of variables of which half are reciprocals of the other half, Schur polynomials can be factorized into products of odd and even orthogonal characters. We also obtain related…
In this paper, we study the Carlitz's degenerate Bernoulli numbers and polynomials and give some formulae and identities related to those numbers and polynomials.
Given a sheaf on a projective space P^n we define a sequence of canonical and easily computable Chow complexes on the Grassmannians of planes in P^n, generalizing the Beilinson monad on P^n. If the sheaf has dimension k, then the Chow form…
This paper has two primary contributions. First, we explore degenerate Sheffer-type polynomials, a hybrid of higher-order degenerate Bernoulli and Euler polynomials, and derive their properties. Second, assuming that the moment generating…
In this paper, applying the Fa\`a di Bruno formula and some properties of Bell polynomials, several closed formulas and determinantal expressions involving Stirling numbers of the second kind for higher-order Bernoulli and Euler polynomials…
Schur's transforms of a polynomial are used to count its roots in the unit disk. These are generalized them by introducing the sequence of symmetric sub-resultants of two polynomials. Although they do have a determinantal definition, we…
Just as the definition of factorial Schur functions as a ratio of determinants allows one to show that they satisfy a Jacobi-Trudi-type identity and have an explicit combinatorial realisation in terms of semistandard tableaux, so we offer…
In previous work, we employed a geometric method of Kazarian to prove Pfaffian formulas for a certain class of degeneracy loci in types B, C, and D. Here we refine that approach to obtain formulas for more general loci, including those…
We study an action of the skew divided difference operators on the Schubert polynomials and give an explicit formula for structural constants for the Schubert polynomials in terms of certain weighted paths in the Bruhat order on the…
In this paper, we give some interesting identities of higher-order Bernoulli, Frobenius-Euler and Euler polynomials arising from umbral calculus. From our method of this paper, we can derive many interesting identities of special…
We prove an explicit degree formula for certain unitary Deligne-Lusztig varieties. Combining with an alternative degree formula in terms of Schubert calculus, we deduce several algebraic combinatorial identities which may be of independent…
A combinatorial construction proves an identity for the product of the Pfaffian of a skew-symmetric matrix by the Pfaffian of one of its submatrices. Several applications of this identity are followed by a brief history of Pfaffians.
In this paper, we study some properties of Sheffer sequences for the powers of Sheffer pairs under umbral composition. From our properties we derive new and interesting identities of Sheffer sequences of special polynomials for the powers…
Let $(p_n)_n$ be a sequence of orthogonal polynomials with respect to the measure $\mu$. Let $T$ be a linear operator acting in the linear space of polynomials $\PP$ and satisfying that $\dgr(T(p))=\dgr(p)-1$, for all polynomial $p$. We…
We generalize linear superalgebra to higher gradings and commutation factors, given by arbitrary abelian groups and bicharacters. Our central tool is an extension, to monoidal categories of modules, of the Nekludova-Scheunert faithful…
We present identities for permutations with fixed points. The formulas are based on successive derivations or integrations of the determinant of a particular matrix.
In this note, by using the Hasse-Teichm\"uller derivatives, we obtain two explicit expressions for the related numbers of higher order Appell polynomials. One of them presents a determinant expression for the related numbers of higher order…
We study a family of polynomials whose values express degrees of Schubert varieties in the generalized complex flag manifold G/B. The polynomials are given by weighted sums over saturated chains in the Bruhat order. We derive several…
There is a remarkable formula for the principal specialization of a type A Schubert polynomial as a weighted sum over reduced words. Taking appropriate limits transforms this to an identity for the backstable Schubert polynomials recently…