22 citations · 45 across the 6 of their papers we have counts for
5 papers · 1 filter
A Salem-Spencer-Type Construction for Large Subsets of Integer Grids with No Isosceles Right Triangles
Gyula Károlyi, Jozsef Solymosi
Let be the largest size of a subset of containing no nondegenerate isosceles right triangle. We give a modified Salem--Spencer-type construction over…
Covering the Permutohedron by Affine Hyperplanes
Gábor Hegedüs, Gyula Károlyi
An almost cover of a finite set in the affine space is a collection of hyperplanes that together cover all points of the set except one. Using the polynomial method, we determine t…
A new approach to constant term identities and Selberg-type integrals
Gyula Károlyi, Zoltán Lóránt Nagy, Fedor Petrov +1
Selberg-type integrals that can be turned into constant term identities for Laurent polynomials arise naturally in conjunction with random matrix models in statistical mechanics. B…
A simple proof of the Zeilberger-Bressoud q-Dyson theorem
Gyula Károlyi, Zoltán Lóránt Nagy
As an application of the Combinatorial Nullstellensatz, we give a short polynomial proof of the q-analogue of Dyson's conjecture formulated by Andrews and first proved by Zeilberge…
Remarks to Arsovski's proof of Snevily's conjecture
Gergely Harcos, Gyula Károlyi, Géza Kós
Based on the recent work of Arsovski, we confirm a conjecture of Feng, Sun, and Xiang, and we give a shortened proof of Snevily's conjecture.