Related papers: On some new hook-content identities

We prove an interesting identity for the sum of determinants, which is a generalization of the sum of a geometric progression. The proof is quite long and a number of other identities are proved along the way. Some of the more elementary…

In this work, we give combinatorial proofs for generating functions of two problems, i.e., flushed partitions and concave compositions of even length. We also give combinatorial interpretation of one problem posed by Sylvester involving…

We give "hybrid" proofs of the $q$-binomial theorem and other identities. The proofs are "hybrid" in the sense that we use partition arguments to prove a restricted version of the theorem, and then use analytic methods (in the form of the…

We present several identities with a form of polynomials or rational functions that involve Pochhammer and q-Pochhammer symbols and q-binomials (i.e. Gauss polynomials). All these identities were obtained by some analytical methods based on…

We propose a new design heuristic to tackle combinatorial optimisation problems, inspired by Hamiltonians for optimal state-transfer. The result is a rapid approximate optimisation algorithm. We provide numerical evidence of the success of…

An identity that is reminiscent of the Littlewood identity plays a fundamental role in recent proofs of the facts that alternating sign triangles are equinumerous with totally symmetric self-complementary plane partitions and that…

Identity verification is the process of confirming an individual's claimed identity, which is essential in sectors like finance, healthcare, and online services to ensure security and prevent fraud. However, current password/PIN-based…

We introduce the difference operator for functions defined on strict partitions and prove a polynomiality property for a summation involving the hook length and content statistics. As an application, several new hook-content formulas for…

In this paper we present a new identity and some of its variants which can be used for finding solutions while solving fractional infinite and finite series. We introduce another simple identity which is capable of generating solutions for…

We naturally obtain some combinatorial identities finding the difference analogs of hyperbolic and trigonometric functions of order $n.$ In particular, we obtain the identities connected with the proved in the paper the addition formulas…

Answering natural language questions on knowledge graphs (KGQA) remains a great challenge in terms of understanding complex questions via multi-hop reasoning. Previous efforts usually exploit large-scale entity-related text corpora or…

Using a probabilistic approach, we derive several interesting identities involving beta functions. Our results generalize certain well-known combinatorial identities involving binomial coefficients and gamma functions.

Recently Z. S. Zhang et al [Phys. Lett. A 356(2006)199] have proposed an one-way quantum identity authentication scheme and claimed that it can verify the user's identity and update securely the initial authentication key for reuse.

We prove astonishing identities generated by compositions of positive integers. In passing, we obtain two new identities for Stirling numbers of the first kind. In the two last sections we clarify an algebraic sense of these identities and…

We prove an identity about partitions, previously conjectured in the study of shifted Jack polynomials (math.CO/9903020). The proof given is using $\lambda$-ring techniques. It would be interesting to obtain a bijective proof.

In a variety of applications, there is a need to authenticate content that has experienced legitimate editing in addition to potential tampering attacks. We develop one formulation of this problem based on a strict notion of security, and…

We provide combinatorial tools inspired by work of Warnaar to give combinatorial interpretations of the sum sides of the Andrews-Gordon and Bressoud identities. More precisely, we give an explicit weight- and length-preserving bijection…

In this brief semi-expository article we present a few efficient techniques for calculating and proving determinantal identities. Several stimulating examples of different flavor and applications are spread across the pages which we hope…

We introduce several new identities combining basic hypergeometric sums and integrals. Such identities appear in the context of superconformal index computations for three-dimensional supersymmetric dual theories. We give both analytic…

An observer-based Hamiltonian identification algorithm for quantum systems is proposed. For the 2-level case an exponential convergence result based on averaging arguments and some relevant transformations is provided. The convergence for…