Algebra / Number Theory / Combinatorics Seminar

Peg solitaire is a popular one person board game that has been played in many countries on various board shapes. Recently, peg solitaire has been studied extensively in two colors on […]

In 1932, Tarski conjectured that a convex body of width 1 can be covered by planks, regions between two parallel hyperplanes, only if the total width of planks is at […]

In this talk we link discrete Markov spectrum to geometry of continued fractions. As a result of that we get a natural generalization of classical Markov tree which leads to an efficient computation of Markov minima for all elements in generalized Markov trees.

I will explain how to apply presentations of algebras (together with some classical results from non-commutative algebra) to obtain some 5 polynomial invariants telling us when two pairs of 2x2 […]

As  $\lambda$ runs through all integer partitions, the set of   Schur functions $\{s_{\lambda}\}_\lambda$ forms a basis in the ring of symmetric functions. Hence the rule $$s_{\lambda}s_{\mu}=\sum c_{\lambda,\mu}^{\gamma} s_{\gamma}$$ makes sense […]