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Motivated in part by hook-content formulas for certain restricted partitions in representation theory, we consider the total number of hooks of fixed length in odd versus distinct partitions. We show that there are more hooks of length $2$,…
We prove that the set of matchings with a fixed number of unmatched vertices is Schur-positive with respect to the set of short chords. Two proofs are presented. The first proof applies a new combinatorial criterion for Schur-positivity,…
The acoustic wave equation is solved in time domain with a boundary element formulation. The time discretisation is performed with the generalised convolution quadrature method and for the spatial approximation standard lowest order…
Carlitz considered integer compositions in which adjacent parts must be unequal. Arndt recently initiated the study of restricted compositions based on conditions applied to certain pairs of parts rather than to individual parts. Here, we…
We propose different methods for alternative representation and visual augmentation of sheet music that help users gain an overview of general structure, repeating patterns, and the similarity of segments. To this end, we explored mapping…
In this note, we show how a combinatorial identity of Frisch can be applied to prove and generalize some well-known identities involving harmonic numbers. We also present some combinatorial identities involving odd harmonic numbers which…
Although cuckoo hashing has significant applications in both theoretical and practical settings, a relevant downside is that it requires lookups to multiple locations. In many settings, where lookups are expensive, cuckoo hashing becomes a…
The typicality approach and the Hilbert space averaging method as its technical manifestation are important concepts of quantum statistical mechanics. Extensively used for expectation values we extend them in this paper to transition…
Classical data encoding is usually treated as a black-box in the oracle-based quantum algorithms. On the other hand, their constructions are crucial for practical algorithm implementations. Here, we open the black-boxes of data encoding and…
CountSketch is a popular dimensionality reduction technique that maps vectors to a lower dimension using randomized linear measurements. The sketch supports recovering $\ell_2$-heavy hitters of a vector (entries with $v[i]^2 \geq…
Several learned policies have been proposed to replace heuristics for scheduling, caching, and other system components in modern systems. By leveraging diverse features, learning from historical trends, and predicting future behaviors, such…
Recently, there has been a lot of work on combinatorial inequalities related to hook-lengths in $t$-regular partitions. In this short note, we give a proof using generating functions for a result proved by Singh and Barman (2026) using…
Leveraging recent progress in physical-layer network coding we propose a new approach to random access: When packets collide, it is possible to recover a linear combination of the packets at the receiver. Over many rounds of transmission,…
Given a probability measure $\mu$ on a set $\mathcal{X}$ and a vector-valued function $\varphi$, a common problem is to construct a discrete probability measure on $\mathcal{X}$ such that the push-forward of these two probability measures…
The high computational complexity of the multiple signal classification (MUSIC) algorithm is mainly caused by the subspace decomposition and spectrum search, especially for frequent real-time applications or massive sensors. In this paper,…
Error-correcting codes that admit local decoding and correcting algorithms have been the focus of much recent research due to their numerous theoretical and practical applications. An important goal is to obtain the best possible tradeoffs…
Given a hypergraph $H$ with $m$ hyperedges and a set $Q$ of $m$ \emph{pinning subspaces}, i.e.\ globally fixed subspaces in Euclidean space $\mathbb{R}^d$, a \emph{pinned subspace-incidence system} is the pair $(H, Q)$, with the constraint…
We consider the admittance of a chaotic quantum dot, capacitively coupled to a gate and connected to two electron reservoirs by multichannel ballistic point contacts. For a dot in the regime of weak-localization and universal conductance…
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…
Concurrent hash tables are one of the most important concurrent data structures with numerous applications. Since hash table accesses can dominate the execution time of the overall application, we need implementations that achieve good…