Search Results - "Romik, Dan"

The Taylor coefficients of the Jacobi theta constant θ3 by Romik, Dan

“…We study the Taylor expansion around the point x = 1 of a classical modular form, the Jacobi theta constant θ 3 . This leads naturally to a new sequence ( d (…”
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The dynamics of Pythagorean Triples by Romik, Dan

“…We construct a piecewise onto 3-to-1 dynamical system on the positive quadrant of the unit circle, such that for rational points (which correspond to…”
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On Viazovska’s modular form inequalities by Romik, Dan

“…Viazovska proved that the E 8 lattice sphere packing is the densest sphere packing in 8 dimensions. Her proof relies on two inequalities between functions…”
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Local extrema in random permutations and the structure of longest alternating subsequences by Romik, Dan

“…Let $\textbf{as}_n$ denote the length of a longest alternating subsequence in a uniformly random permutation of order $n$. Stanley studied the distribution of…”
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The Taylor coefficients of the Jacobi theta constant $$\theta _3 by Romik, Dan

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Differential Equations and Exact Solutions in the Moving Sofa Problem by Romik, Dan

“…The moving sofa problem, posed by Moser in 1966, asks for the planar shape of maximal area that can move around a right-angled corner in a hallway of unit…”
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Connectivity Patterns in Loop Percolation I: the Rationality Phenomenon and Constant Term Identities by Romik, Dan

“…Loop percolation, also known as the dense O (1) loop model, is a variant of critical bond percolation in the square lattice Z 2 whose graph structure consists…”
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Permutations with short monotone subsequences by Romik, Dan

“…We consider permutations of $1,2,...,n^2$ whose longest monotone subsequence is of length $n$ and are therefore extremal for the Erdős-Szekeres Theorem. Such…”
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Integrals, partitions, and cellular automata by Holroyd, Alexander E., Liggett, Thomas M., Romik, Dan

“…We prove that \begin{equation*}\int_0^1\frac{-\log f(x)}xdx=\frac{\pi^2}{3ab},\end{equation*} where f(x) is the decreasing function that satisfies…”
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Absorbing time asymptotics in the oriented swap process by Bufetov, Alexey, Gorin, Vadim, Romik, Dan

“…The oriented swap process is a natural directed random walk on the symmetric group that can be interpreted as a multispecies version of the totally asymmetric…”
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ARCTIC CIRCLES, DOMINO TILINGS AND SQUARE YOUNG TABLEAUX by Romik, Dan

“…The arctic circle theorem of Jockusch, Propp, and Shor asserts that uniformly random domino tilings of an Aztec diamond of high order are frozen with…”
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JEU DE TAQUIN DYNAMICS ON INFINITE YOUNG TABLEAUX AND SECOND CLASS PARTICLES by Romik, Dan, Śniady, Piotr

“…We study an infinite version of the "jeu de taquin" sliding game, which can be thought of as a natural measure-preserving transformation on the set of infinite…”
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The oriented swap process and last passage percolation by Bisi, Elia, Cunden, Fabio Deelan, Gibbons, Shane, Romik, Dan

“…We present new probabilistic and combinatorial identities relating three random processes: the oriented swap process (OSP) on n particles, the corner growth…”
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New enumeration formulas for alternating sign matrices and square ice partition functions by Ayyer, Arvind, Romik, Dan

“…The refined enumeration of alternating sign matrices (ASMs) of given order having prescribed behavior near one or more of their boundary edges has been the…”
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Enumeration formulas for young tableaux in a diagonal strip by Baryshnikov, Yuliy, Romik, Dan

“…We derive combinatorial identities, involving the Bernoulli and Euler numbers, for the numbers of standard Young tableaux of certain skew shapes. This…”
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More refined enumerations of alternating sign matrices by Fischer, Ilse, Romik, Dan

“…We study a further refinement of the standard refined enumeration of alternating sign matrices (ASMs) according to their first two rows instead of just the…”
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On Viazovska's modular form inequalities by Romik, Dan

“…Viazovska proved that the $E_8$ lattice sphere packing is the densest sphere packing in 8 dimensions. Her proof relies on two inequalities between functions…”
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Limit shapes of bumping routes in the Robinson-Schensted correspondence by Romik, Dan, Śniady, Piotr

“…We prove a limit shape theorem describing the asymptotic shape of bumping routes when the Robinson–Schensted algorithm is applied to a finite sequence of…”
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Limit shapes for random square Young tableaux by Pittel, Boris, Romik, Dan

“…Our main result is a limit shape theorem for the two-dimensional surface defined by a uniform random n × n square Young tableau. The analysis leads to a…”
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Permutations with short monotone subsequences by Romik, Dan

“…We consider permutations of 1 , 2 , … , n 2 whose longest monotone subsequence is of length n and are therefore extremal for the Erdős–Szekeres theorem. Such…”
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