Proof of Ira Gessel's Lattice Path Conjecture

Proof of Lemma 6.3 in ``The crossing number of $K_{4,n}$ on the torus and the Klein bottle"

Proof of Razumov-Stroganov conjecture for some infinite families of link patterns

Proof of Stanley's conjecture about irreducible character values of the symmetric group

Proof of the Alternating Sign Matrix Conjecture

Proof of the Lovasz Conjecture

Proof of the monotone column permanent conjecture

Proof of the Razumov-Stroganov conjecture

Proof of the Refined Alternating Sign Matrix Conjecture

Proof of the Somos-4 Hankel Determinants Conjecture

Proof of two conjectures of Zuber on fully packed loop configurations

Proofs of some binomial identities using the method of last squares

Proofs of two conjectures of Kenyon and Wilson on Dyck tilings

Proofs of two conjectures on ternary weakly regular bent functions

Proofs of Two Conjectures On the Dimensions of Binary Codes

Proper and Unit Trapezoid Orders and Graphs

Proper partitions of a polygon and k-Catalan numbers

Proper path-factors and interval edge-coloring of (3,4)-biregular bigraphs

Properly coloured copies and rainbow copies of large graphs with small maximum degree

Properties of $θ$-super positive graphs