Related papers: A short proof of Combinatorial Nullstellensatz
We present a short new proof of the canonical polynomial van der Waerden theorem, recently established by Girao [arXiv:2004.07766].
We give a simple proof of a recently result concerning Hardy $q$-inequalities.
In this paper, we present the Nullstellensatz in case of the coordinate rings of a nonempty subset of Kn where K is a finite field Fq. Some applications of the Nullstellensatz are also discussed.
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…
In this paper, we present the simple components of the Wedderburn decomposition of semisimple commutative group algebras over finite abelian groups, which we investigate from a geometric point of view. We also present the Wedderburn…
We significantly strengthen and generalize the theorem lifting Nullstellensatz degree to monotone span program size by Pitassi and Robere (2018) so that it works for any gadget with high enough rank, in particular, for useful gadgets such…
In this note, we use the method of [3] to give a simple proof of famous Witten conjecture. Combining the coefficients derived in our note and this method, we can derive more recursion formulas of Hodge integrals.
In this note, we provide a short proof of Feige's conjecture for identically distributed random variables.
A proof is given of Rosenthal's \(\ell_1\) theorem.
In this note we present examples of cumulative connection constants included new fibonomial ones. All examples posses combinatorial interpretation.
This is a short note on the log canonical inversion of adjunction.
We present an elementary combinatorial proof of the celebrated Friendship theorem. The proof involves looking at independent sets and constructing a bound on their size which forces a contradiction.
We provide a simple proof of the radial symmetry of any nonnegative minimizer for a general class of quasi-linear minimization problems.
We give an elementary, self-contained, and purely combinatorial proof of the Rayleigh monotonicity property of graphs.
We construct a combinatorially large measure zero subset of the Cantor set.
Combinatorial number system represents a non-negative natural numbers as sum of binomial coefficients. This paper presents an induction proof that there exists unique representation of every non-negative natural number $m$ as sum of $r$…
This note presents an elementary and direct proof for the convexity of the Choquet integral when the corresponding set function is submodular.
In this paper, we propose a generalization of a congruence due to Carlitz.
Systems of polynomial equations over an algebraically-closed field K can be used to concisely model many combinatorial problems. In this way, a combinatorial problem is feasible (e.g., a graph is 3-colorable, hamiltonian, etc.) if and only…
In this note, we give a simple method for computing the column sums of the Sonnenschein summability matrices.