11 citations · 15 across the 11 of their papers we have counts for
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Difference sets in Quadratic Density Hales Jewett conjecture with 2 letters
Aritro Pathak
The Quadratic Density Hales Jewett conjecture with letters states that for large enough , every dense subset of contains a combinatorial line where the wil…
Marstrand type slicing statements in are false for the counting dimension
Aritro Pathak
We show that for separated subsets of , the natural Marstrand type slicing statements are false with the counting dimension that was used earlier by Moreira and Lima an…
A Marstrand type slicing theorem for subsets of with the mass dimension
Aritro Pathak
We prove a Marstrand type slicing theorem for the subsets of the integer square lattice. This problem is the dual of the corresponding projection theorem, which was considered by G…
Sums of powers, and products of elements of the middle third Cantor set
Aritro Pathak
The questions of the measure and finding open intervals in certain sets of sums and products of elements of the middle third Cantor set (or a variant of it), have generated conside…
On certain partition bijections related to Euler's partition problem
Aritro Pathak
We give short elementary expositions of combinatorial proofs of some variants of Euler's partitition problem that were first addressed analytically by George Andrews, and later com…
Glaisher's Partition problem
Aritro Pathak
We generalize the well known Glaisher partition bijection result. For given positive integers n, d, both greater than 1, we provide a rich family of bijections between the set of p…