Sergi Elizalde

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math.CO2026

Penney's game for permutations

Sergi Elizalde, Yixin Lin

We consider the permutation analogue of Penney's game for words. Two players, in order, each choose a permutation of length $k \geq 3$ ; then a sequence of independent random values fr…

math.CO2026

Necklaces, subset sums, and cyclic permutations

Robert Dougherty-Bliss, Sergi Elizalde

It is a well known that, for odd $n$ , the number of subsets of ${1, 2, \dots, n}$ the sum of whose elements is divisible by $n$ equals the number of binary necklaces of length $n$ .…

math.CO2026

Pattern avoidance in nonnesting permutations

Sergi Elizalde, Amya Luo

Nonnesting permutations are permutations of the multiset ${1, 1, 2, 2, \dots, n, n}$ that avoid subsequences of the form $abba$ for any $a \neq = b$ . These permutations have recently been…

math.CO2025

A bijection for descent sets of permutations with only even and only odd cycles

Sergi Elizalde

It is known that, when $n$ is even, the number of permutations of ${1, 2, \dots, n}$ all of whose cycles have odd length equals the number of those all of whose cycles have even len…

math.CO2025

Symmetry of ascent and descent distributions on rectangular and staircase tableaux

Sergi Elizalde

We give direct bijective proofs of the symmetry of the distributions of the number of ascents and descents over standard Young tableaux of shape $I^»$ , where $I^»$ is a rectangle $(n…

math.CO2024

Canon permutations and generalized descents of standard Young tableaux

Sergi Elizalde

Canon permutations are permutations of the multiset having $k$ copies of each integer between $1$ and $n$ , with the property that the subsequences obtained by taking the $j$ th copy…