Over the past 25 years, there has been an explosion of interest in the area of random tilings.
The first book devoted to the topic, this timely text describes the mathematical theory of …

The celebrated hook-length formula gives a product formula for the number of standard
Young tableaux of a straight shape. In 2014, Naruse announced a more general formula for …

A log Calabi–Yau surface with maximal boundary, or Looijenga pair, is a pair (Y, D) with Y a
smooth rational projective complex surface and D= D 1+⋯+ D l∈|− KY| an anticanonical …

Can you decide if there is a coincidence in the numbers counting two different combinatorial
objects? For example, can you decide if two regions in R 3 have the same number of …

Our work deals with symmetric rational functions and probabilistic models based on the fully
inhomogeneous six vertex (ice type) model satisfying the free fermion condition. Two …

We give new bounds and asymptotic estimates for Kronecker and Littlewood–Richardson
coefficients. Notably, we resolve Stanley's questions on the shape of partitions attaining the …

arxiv:1803.06636v2 [math.CO] 31 Mar 2018 Page 1 arxiv:1803.06636v2 [math.CO] 31 Mar
2018 COMPLEXITY PROBLEMS IN ENUMERATIVE COMBINATORICS IGOR PAK⋆ Abstract …

The classical 1991 result by Brightwell and Winkler states that the number of linear
extensions of a poset is# P-complete. We extend this result to posets with certain restrictions …

In this paper, we study large time large deviations for the height function $\mathfrak {h}(x, t) $
of the $ q $-deformed polynuclear growth introduced in ABW22 [arxiv: 2108.06018]. We …

The Naruse hook-length formula is a recent general formula for the number of standard
Young tableaux of skew shapes, given as a positive sum over excited diagrams of products …