Related papers: On some new hook-content identities
We propose and prove a new polynomial identity that implies Schur's partition theorem. We give combinatorial interpretations of some of our expressions in the spirit of Kur\c{s}ung\"oz. We also present some related polynomial and $q$-series…
Two-party one-way quantum communication has been extensively studied in the recent literature. We target the size of minimal information that is necessary for a feasible party to finish a given combinatorial task, such as distinction of…
We give a proof of a recent combinatorial conjecture due to the first author, which was discovered in the framework of commutative algebra. This result gives rise to new companions to the famous Andrews-Gordon identities. Our tools involve…
We present a new twist on an old identity.
In this paper, we provide combinatorial proofs for certain partition identities which arise naturally in the context of Langlands' beyond endoscopy proposal. These partition identities motivate an explicit plethysm expansion of…
I consider the use of entanglement between two parties to enable one to authenticate her identity to another over a quantum communication channel. Exploiting the phenomenon of entanglement-catalyzed transformations between pure states gives…
Quantum information theory is a very young area of research offering a lot of challenging open questions to be tackled by ambitious upcoming physicists. One such problem is addressed in this thesis. Recently, several protocols have emerged…
We present a novel blockchain based service for proving the provenance of online digital identity, exposed as an assistive tool to help non-expert users make better decisions about whom to trust online. Our service harnesses the digital…
We show a new proof for the load of obtained by a Cuckoo Hashing data structure. Our proof is arguably simpler than previous proofs and allows for new generalizations. The proof first appeared in Pinkas et. al. \cite{PSWW19} in the context…
We introduce dilogarithm identities through a beta integral-based technique that we apply to provide analytic proofs of previously conjectured dilogarithm relations, solving open problems given by both Bytsko and Campbell, and that we…
We give some new identities for (h; q)-Genocchi numbers and polynomials by means of the fermionic p-adic q-integral on Zp and the weighted q-Bernstein polynomials.
To what extent do individual eigenstates encode information of their underlying Hamiltonian, and how does this depend on their spectral position? For many-body quantum systems, this issue is widely understood in terms of the differing…
We present a novel framework for studying combinatorial identities through the geometric lens of subset distributions in q-valued cubes. By analyzing how elements of arbitrary subsets are distributed among the faces of the cube E_q^n, we…
We present a new partition identity and give a combinatorial proof of our result. This generalizes a result of Andrew's in which he considers the generation function for partitions with respect to size, number of odd parts, and number of…
We review the development of the quantum version of Ahlswede and Dueck's theory of identification via channels. As is often the case in quantum probability, there is not just one but several quantizations: we know at least two different…
Traditional authentication systems that rely on simple passwords, PIN numbers or tokens have many security issues, like easily guessed passwords, PIN numbers written on the back of cards, etc. Thus, biometric authentication methods that…
A secure quantum identification system combining a classical identification procedure and quantum key distribution is proposed. Each identification sequence is always used just once and new sequences are ``refuelled'' from a shared provably…
This paper proposes a new problem of complementary evidence identification for open-domain question answering (QA). The problem aims to efficiently find a small set of passages that covers full evidence from multiple aspects as to answer a…
We develop the notion of a locally homomorphic channel and prove an approximate equivalence between those and codes for computing functions. Further, we derive decomposition properties of locally homomorphic channels which we use to analyze…
Digital identity is unsolved: after many years of research there is still no trusted communication over the Internet. To provide identity within the context of mutual distrust, this paper presents a blockchain-based digital identity…