We provide combinatorial proofs of some of the q-series identities considered by Andrews, Jimenez-Urroz and Ono [q-series identities and values of certain $L$-functions. Duke Math. J. 108 (2001), no. 3, 395--419]....
Combinatorial topology is the older name for algebraic topology when all topological problems were expressed, set up and solved in Euclidean space of dimensions 1,2 and 3.
May 23, 2012 · Just FYI, what you call a "logical proof" is known as a "combinatorial proof", and such a proof is perfectly valid and often very insightful. What I suspect you mean by "mathematical proof" is …
This paper studies the distribution of the component spectrum of combinatorial structures such as uniform random forests, in which the classical generating function for the numbers of (irreducible) elements of the different sizes converges at the r...
We introduce a misere quotient semigroup construction in impartial combinatorial game theory, and argue that it is the long-sought natural generalization of the normal-play Sprague-Grundy theory to misere play. Along the way, we illustrate how to u...
Vehicle Routing Problems (VRPs) are significant Combinatorial Optimization (CO) problems holding substantial practical importance. Recently, Neural Combinatorial Optimization (NCO), which involves training deep learning models on extensive data to le...
The current art in optimal combinatorial auctions is limited to handling the case of single units of multiple items, with each bidder bidding on exactly one bundle (single minded bidders). This paper extends the current art by proposing an optimal...
We developed a low-cost, high-throughput microbiome profiling method that uses combinatorial sequence tags attached to PCR primers that amplify the rRNA V6 region. Amplified PCR products are sequenced using an Illumina paired-end protocol to generate...
Graph-based diffusion models have shown promising results in terms of generating high-quality solutions to NP-complete (NPC) combinatorial optimization (CO) problems. However, those models are often inefficient in inference, due to the iterative eval...
A 2-join is an edge cutset that naturally appears in decomposition of several classes of graphs closed under taking induced subgraphs, such as perfect graphs and claw-free graphs. In this paper we construct combinatorial polynomial time algorithms fo...
Reid's recipe for a finite abelian subgroup $G\subset \text{SL}(3,\mathbb{C})$ is a combinatorial procedure that marks the toric fan of the $G$-Hilbert scheme with irreducible representations of $G$. The geometric McKay correspondence conjecture of C...
Recently, Han obtained two hook length formulas for binary trees and asked for combinatorial proofs. One of Han's formulas has been generalized to k-ary trees by Yang. Sagan has found a probabilistic proof of Yang's extension. We give combinatorial p...
We define combinatorial counterparts to the geometric string vertices of Sen-Zwiebach and Costello-Zwiebach, which are certain closed subsets of the moduli spaces of curves. Our combinatorial vertices contain the same information as the geometric one...
We prove some combinatorial identities using the Polya urn and the closely related Hoppe urn....
We examine an important combinatorial challenge in clearing clutter using a mobile robot equipped with a manipulator, seeking to compute an optimal object removal sequence for minimizing the task completion time, assuming that each object is grasped...
In this paper we prove, that none of the three combinatorial 8- manifolds on 15 vertices constructed by Brehm and Kuhnel, each of which is a cohomology quaternionic projective plane, can be combinatorially embedded in the Euclidean 12-space, though t...
We study the inefficiency of mixed equilibria, expressed as the price of anarchy, of all-pay auctions in three different environments: combinatorial, multi-unit and single-item auctions. First, we consider item-bidding combinatorial auctions where m...
Symmetries of combinatorial objects are known to complicate search algorithms, but such obstacles can often be removed by detecting symmetries early and discarding symmetric subproblems. Canonical labeling of combinatorial objects facilitates easy eq...
Phase transitions in combinatorial problems have recently been shown to be useful in locating "hard" instances of combinatorial problems. The connection between computational complexity and the existence of phase transitions has been addressed in S...
For Bayesian combinatorial auctions, we present a general framework for approximately reducing the mechanism design problem for multiple buyers to single buyer sub-problems. Our framework can be applied to any setting which roughly satisfies the foll...