Related papers: On some new hook-content identities

We study a family of inhomogeneous Ising chain models along with an equivalent family of nearest neighbour particle systems. By the correspondence between the two families we prove identities of combinatorial significance relating to…

We present new proofs of two identities arising in the work of Mourad Ismail using partition theoretic generating function interpretations.

A probability method is provided to prove three classes of combinatorial identities. The method is extremely simple, only one step after the proper probability setup.

We give a purely combinatorial proof of the Glaisher-Crofton identity which derives from the analysis of discrete structures generated by iterated second derivative. The argument illustrates utility of symbolic and generating function…

Based on a bijection due to Fu and Tang, we provide combinatorial proofs of several partition identities of Andrews and Merca. We also introduce two weights for partitions to extend one of these identities.

In this paper, we discuss content and context for quantum properties. We give some examples of why quantum properties are problematic: they depend on the context in a non-trivial way. We then connect this difficulty with properties to the…

The restricted partitions in which the largest part is less than or equal to $N$ and the number of parts is less than or equal to $k$ were investigated by Andrews in \cite{Andrews76}. These partitions were extended recently by the author to…

We prove a family of partition identities which is "dual" to the family of Andrews-Gordon's identities. These identities are inspired by a correspondence between a special type of partitions and "hypergraphs" and their proof uses…

There are quantum circuit identities that simplify quantum circuits, reducing the effort needed physically to implement them. This paper constructs all identities made from 3 or fewer operations taken from a common set of one qubit…

We present a proof of a combinatorial conjecture from the second author's Ph.D. thesis. The proof relies on binomial and multinomial sums identities. We also discuss the relevance of the conjecture in the context of PAC-Bayesian machine…

The ongoing regulation of blockchain-based services and applications requires the identification of users who are issuing transactions on the blockchain. This systematic review explores the current status, identifies research gaps, and…

Recently, Pankaj Jyoti Mahanta and Manjil P. Saikika proved some identities relating certain restricted partitions into distinct odd parts with the partition whose odd parts are distinct combinatorially. They asked for the q-series proofs.…

Recently Andrews and Bachraoui proved identities relating certain restricted partitions into distinct even parts with restricted 4-regular partitions by the theory of basic hypergeometric series. They also posed a question regarding…

We give a combinatorial proof via a sign-reversing involution for a new identity that generalizes both the Hockey Stick Identity and the Big Hockey Stick and Pucks Identity.

This research explores the integration of language embeddings for active learning in autonomous driving datasets, with a focus on novelty detection. Novelty arises from unexpected scenarios that autonomous vehicles struggle to navigate,…

Understanding searchers' queries is an essential component of semantic search systems. In many cases, search queries involve specific attributes of an entity in a knowledge base (KB), which can be further used to find query answers. In this…

The first generation of cryptocurrencies introduced revolutionary concepts, yet faced challenges in privacy and regulatory compliance. While subsequent cryptocurrencies aimed to address privacy concerns (like Zcash and Monero), they often…

We exhibit a bijection between recently-introduced combinatorial objects known as valid hook configurations and certain weighted set partitions. When restricting our attention to set partitions that are matchings, we obtain three new…

We establish a construction of optimal authentication codes achieving perfect multi-fold secrecy by means of combinatorial designs. This continues the author's work (ISIT 2009) and answers an open question posed therein. As an application,…

Identity work in Human-Computer Interaction (HCI) has focused on the marginalized group to explore designs to support their asset (what they have). However, little has been explored specifically on the identity work of people with…