Profile classes and partial well-order for permutations.
Profiles of permutations.
Projective bundles.
Projective planes of order 10 do not have a collineation of order 3.
Projective representations of generalized symmetric groups.
Promotion and evacuation on standard Young tableaux of rectangle and staircase shape.
Promotion operator on rigged configurations of type .
Proof of a conjecture of Chan, Robbins, and Yuen.
Proof of a conjecture of Hirschhorn and Sellers on overpartitions
Let p̅(n) denote the number of overpartitions of n. It was conjectured by Hirschhorn and Sellers that p̅(40n+35) ≡ 0 (mod 40) for n ≥ 0. Employing 2-dissection formulas of theta functions due to Ramanujan, and Hirschhorn and Sellers, we obtain a generating function for p̅(40n+35) modulo 5. Using the (p, k)-parametrization of theta functions given by Alaca, Alaca and Williams, we prove the congruence p̅(40n+35) ≡ 0 (mod 5) for n ≥ 0. Combining this congruence and the congruence p̅(4n+3) ≡ 0 (mod...
Proof of a conjectured three-valued family of Weil sums of binomials
We consider Weil sums of binomials of the form , where F is a finite field, ψ: F → ℂ is the canonical additive character, , and . If we fix F and d, and examine the values of as a runs through , we always obtain at least three distinct values unless d is degenerate (a power of the characteristic of F modulo ). Choices of F and d for which we obtain only three values are quite rare and desirable in a wide variety of applications. We show that if F is a field of order 3ⁿ with n odd, and with...
Proof of a determinant evaluation conjectured by Bombieri, Hunt and van Poorten.
Proof of an intersection theorem via graph homomorphisms.
Proof of Conway's lost cosmological theorem.
Proof of Simoes-Pereira's conjectures on locally k-degenerate graphs.
Proof of the alternating sign matrix conjecture.
Proof of the Macdonald Conjecture.
Proof of the conjecture for large .
Proof of the Razumov-Stroganov conjecture for some infinite families of link patterns.
Proof of the refined alternating sign matrix conjecture.
Proof trees for weak achievement games.