Related papers: A Remark on the Higher Capelli Identities
Expository observation on the $\mu$-invariant of singularity models for Ricci Flow.
We present a simple iteration for the Lebesgue identity on partitions, which leads to a refinement involving the alternating sums of partitions.
In this paper we give a simple, short, and self-contained proof for a non-trivial upper bound on the probability that a random $\pm 1$ symmetric matrix is singular.
New identities and congruences involving the ranks and cranks of partitions are proved. The proof depends on a new partial differential equation connecting their generating functions.
In the process of studying a conjecture of Holly M. Green and Martin W. Liebeck, we obtain two interesting identities by elementary methods, one is a combinatorial identity, and the other is a number theoretic identity.
In this note, after recalling a proof of the Macdonald identities for untwisted affine root systems, we derive the Macdonald identities for twisted affine root systems.
An algebraical background of the Lattice Conformal Field Theory is refined with the help of a novel $q$-exponential identity.
We derive two new identities involving the Bernoulli numbers, the Euler numbers, and the Stirling numbers of the first kind using analytic continuation of a well known identity for the Stirling numbers of the first kind.
We give a characterization of connected solvable groups in terms of the existence of representations with certain geometric properties. The existence of such representations for the group of upper triangular matrices played an important…
The purpose of this paper is to give some new identities for the Bernoulli, the Euler and the Genocchi numbers and polynomials.
We provide a simple proof of Kamp's theorem.
We prove a better coloring theorem for aleph_4 and even aleph_3. This has a general topology consequence.
In this paper, we establish an identity for Bernoulli's generalized polynomials. We deduce generalizations for many relations involving classical Bernoulli numbers or polynomials. In particular, we generalize a recent Gessel identity.
A combinatorial identity that was needed in Ahlgren and Ono's proof of a certain congruence conjecture of Frits Beukers is stated, and a pointer to its WZ proof is given.
Recently, Andrews and EI Bachraoui discovered several companions for some famous $q$-series formulas, and derived some new identities involving partitions and overpartitions with distinct parts. In this paper, we shall refine their results…
By means of the generating function method, a linear recurrence relation is explicitly resolved. The solution is expressed in terms of the Stirling numbers of both the first and the second kind. Two remarkable pairs of combinatorial…
An identity is proved connecting two finite sums of inverse tangents. This identity is discretized version of Jacobi's imaginary transformation for the modular angle from the theory of elliptic functions. Some other related identities are…
We present a short proof of Reisner's Theorem, characterizing which simplicial complexes have a Cohen-Macaulay face ring. In some cases, we can also express some homological invariants of the face ring in terms of the reduced homology of…
We derive a new Fibonacci identity. This single identity subsumes important known identities such as those of Catalan, Ruggles, Halton and others, as well as standard general identities found in the books by Vajda, Koshy and others. We also…
We describe those unipotent representations of a finite group of Lie type which are defined over the rational numbers.