Note on expanding implicit functions into formal power series by means of multivariable Stirling polynomials

Fuente: arXiv

Gespeichert in:

Bibliographische Detailangaben
1. Verfasser:	Schreiber, Alfred
Format:	Preprint
Veröffentlicht:	2023
Schlagworte:	Combinatorics Primary: 13F25, 11B83, Secondary: 05A19, 11C08
Online-Zugang:	Acceder al recurso
Tags:	Tag hinzufügen Keine Tags, Fügen Sie den ersten Tag hinzu!

Ähnliche Einträge

Several series expansions for real powers and several formulas for partial Bell polynomials of sinc and sinhc functions in terms of central factorial and Stirling numbers of second kind
von: Qi, Feng, et al.
Veröffentlicht: (2022)

Generalized cyclotomic polynomials associated with regular systems of divisors and arbitrary sets of positive integers
von: Tóth, László
Veröffentlicht: (2024)

A correction to a result of Chinburg and Henriksen on powers of integer polynomials
von: Zhu, Daniel G.
Veröffentlicht: (2024)

Multiplicative congruences for Andrews's even parts below odd parts function and related infinite products
von: Garvan, Frank, et al.
Veröffentlicht: (2025)

Congruence families modulo powers of $7$ for $4$-colored generalized Frobenius partitions
von: Wang, Kangyu, et al.
Veröffentlicht: (2025)

On Gauss-Kraitchik formula for cyclotomic polynomials via symmetric functions
von: Yamada, Tomohiro
Veröffentlicht: (2024)

Transformation properties of Andrews-Beck $NT$ functions and generalized Appell-Lerch series
von: Chen, Rong, et al.
Veröffentlicht: (2024)

Pseudo-involutions in the Riordan group and Chebyshev polynomials
von: Burstein, Alexander, et al.
Veröffentlicht: (2025)

Generalization of Ramanujan's formula for sums of half-integer powers of consecutive integers via formal Bernoulli series
von: Alekseyev, Max A., et al.
Veröffentlicht: (2025)

Polynomials assuming only local prime powers
von: Koprowski, Przemysław
Veröffentlicht: (2025)

On Certain Polytopes Associated to Products of Algebraic Integer Conjugates
von: Albayrak, Seda, et al.
Veröffentlicht: (2024)

On a Family of Nested Recurrences and Their Arithmetical Solutions
von: Cloitre, Benoit
Veröffentlicht: (2025)

Irreducible integer-valued polynomials with prescribed minimal power that factors non-uniquely
von: Nakato, Sarah, et al.
Veröffentlicht: (2024)

On Heights and Diameters of Ternary Cyclotomic and Inclusion-Exclusion Polynomials
von: Bachman, Gennady
Veröffentlicht: (2026)

The arithmetic of critical values I: equicritical quartic polynomials
von: Naccarato, Francesco
Veröffentlicht: (2024)

Power series expansion of Wilf function
von: Qi, Feng
Veröffentlicht: (2021)

Enumeration modulo 4 of overpartitions wherein only even parts can be overlined
von: Carlson, Aidan, et al.
Veröffentlicht: (2024)

Logarithmic Newton polygons and polytopes, and the factorization of Dirichlet polynomials
von: Bonciocat, Nicolae Ciprian
Veröffentlicht: (2025)

Restricted sumsets in multiplicative subgroups
von: Yip, Chi Hoi
Veröffentlicht: (2023)

Some power series extensions of Fibonacci and Lucas polynomials
von: Cigler, Johann
Veröffentlicht: (2025)

Infinite product of power series
von: Chen, Kui-Yo, et al.
Veröffentlicht: (2023)

On the Number of Regular Integers Modulo $n$ and Its Significance for Cryptography
von: Dohmen, Klaus, et al.
Veröffentlicht: (2023)

The Schur polynomials in all primitive $n$th roots of unity
von: Hidaka, Masaki, et al.
Veröffentlicht: (2024)

Partitions With Designated Summands Not Divisible by $2^l$, $2$, and $3^l$ Modulo $2$, $4$, and $3$
von: Herden, Daniel, et al.
Veröffentlicht: (2021)

Critical probabilistic characteristics of the Cramér model for primes and arithmetical properties
von: Weber, Michel
Veröffentlicht: (2021)

Primes in LCM recurrences
von: Cloitre, Benoit
Veröffentlicht: (2025)

The congruence properties of Romik's sequence of Taylor coefficients of Jacobi's theta function $θ_3$
von: Krattenthaler, Christian, et al.
Veröffentlicht: (2023)

Domination Polynomial of the Rook Graph
von: Mertens, Stephan
Veröffentlicht: (2024)

An explicit algebraic generating function for OEIS A348410
von: Niu, Tong
Veröffentlicht: (2026)

Determinants of modular Collatz graphs and variants
von: Karras, Achilleas, et al.
Veröffentlicht: (2026)

Primes and absolutely or non-absolutely irreducible elements in atomic domains
von: Fadinger, Victor, et al.
Veröffentlicht: (2024)

Notes on Riordan arrays and lattice paths
von: Barry, Paul
Veröffentlicht: (2025)

Rook decomposition of the Partition function
von: Sharan, N. Guru
Veröffentlicht: (2025)

Dold-Gauss Congruences, Norm Descent, and Rational Rigidity
von: Bal, Hartosh Singh
Veröffentlicht: (2025)

An Exploration of Crank Generating functions for $t$-core partitions
von: Wilson, Samuel
Veröffentlicht: (2026)

Counting (skew-)reciprocal Littlewood polynomials with square discriminant
von: Hokken, David
Veröffentlicht: (2023)

Correspondence among congruence families for generalized Frobenius partitions via modular permutations
von: Chen, Rong, et al.
Veröffentlicht: (2025)

Multiple breaks of log-concavity in the independence polynomials of trees
von: Bautista-Ramos, César
Veröffentlicht: (2025)

A Note on the Number of Representations of $n$ as a Sum of Generalized Polygonal Numbers
von: Bandyopadhyay, Subhajit, et al.
Veröffentlicht: (2024)

Explicit formulae for generalized Stirling and Eulerian numbers
von: Küstner, Josef
Veröffentlicht: (2024)

if (filemtime($filename) + $maxlifetime < time()) { unlink($filename); $count++; } } return $count; } /** * A function that is called internally when session data is to be saved. * * @param string $sessId The current session ID * @param string $data The session data to write * * @return bool */ protected function saveSession($sessId, $data): bool { $sessFile = $this->path . '/sess_' . $sessId; if ($handle = fopen($sessFile, 'w')) { $return = false; // Lock the file for exclusive access to avoid issues with multiple // processes writing session simultaneously: if (flock($handle, LOCK_EX)) { $return = fwrite($handle, $data); // Make sure that there's no trailing data by truncating the file to // the correct length: ftruncate($handle, strlen($data)); fflush($handle); flock($handle, LOCK_UN); } fclose($handle); if ($return !== false) { return true; } } // If we got this far, something went wrong with the file output... // It is tempting to throw an exception here, but this code is called // outside of the context of exception handling, so all we can do is // echo a message.

// Anecdotal testing Today and Yesterday seems to indicate destroy() // is called by the garbage collector and everything is good. // Something to keep in mind though. return 0; } /** * Write function that is called when session data is to be saved. * * @param string $sessId The current session ID * @param string $data The session data to write * * @return bool */ public function write($sessId, $data): bool { if ($this->writesDisabled) { return true; } return $this->saveSession($sessId, $data); } /** * A function that is called internally when session data is to be saved. * * @param string $sessId The current session ID * @param string $data The session data to write * * @return bool */ abstract protected function saveSession($sessId, $data): bool; }

* * @return void */ public function writeClose() { // The assumption is that we're using PHP's ext/session. // session_write_close() will actually overwrite $_SESSION with an // empty array on completion -- which leads to a mismatch between what // is in the storage object and $_SESSION. To get around this, we // temporarily reset $_SESSION to an array, and then re-link it to // the storage object. // // Additionally, while you _can_ write to $_SESSION following a // session_write_close() operation, no changes made to it will be // flushed to the session handler. As such, we now mark the storage // object isImmutable. $storage = $this->getStorage(); if (! $storage->isImmutable()) { $_SESSION = $storage->toArray(true); session_write_close(); $storage->fromArray($_SESSION); $storage->markImmutable(); } } /** * Attempt to set the session name * * If the session has already been started, or if the name provided fails * validation, an exception will be raised. * * @param string $name * @return SessionManager * @throws Exception\InvalidArgumentException */ public function setName($name) { if ($this->sessionExists()) { throw new Exception\InvalidArgumentException( 'Cannot set session name after a session has already started'

Environment & details:

GET Data empty

POST Data empty

Files empty

Key	Value
ui	"standard"
VUFIND_SESSION	"2f0fbd399897753c3173fd07b451c9ec"
language	"de"

Session

Key	Value
__Laminas	array:2 [`"_REQUEST_ACCESS_TIME" => 1790734978.722 "_VALID" => array:1 [ "Laminas\Session\Validator\Id" => "2f0fbd399897753c3173fd07b451c9ec" ]`]
SessionState	Laminas\Stdlib\ArrayObject {#938}
FlashMessenger	Laminas\Stdlib\ArrayObject {#1433}
SessionHelper	Laminas\Stdlib\ArrayObject {#1759}

Server/Request Data

Key	Value
REDIRECT_VUFIND_LOCAL_DIR	"/usr/local/vufind/local"
REDIRECT_HTTPS	"on"
REDIRECT_SSL_TLS_SNI	"info.umar.mx"
REDIRECT_STATUS	"200"
VUFIND_LOCAL_DIR	"/usr/local/vufind/local"
HTTPS	"on"
SSL_TLS_SNI	"info.umar.mx"
HTTP_ACCEPT	"/"
HTTP_USER_AGENT	"Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)"
HTTP_COOKIE	"ui=standard; VUFIND_SESSION=2f0fbd399897753c3173fd07b451c9ec; language=de"
HTTP_ACCEPT_ENCODING	"gzip, br, zstd, deflate"
HTTP_HOST	"info.umar.mx"
PATH	"/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/snap/bin"
SERVER_SIGNATURE	"<address>Apache/2.4.66 (Ubuntu) Server at info.umar.mx Port 443</address>\n"
SERVER_SOFTWARE	"Apache/2.4.66 (Ubuntu)"
SERVER_NAME	"info.umar.mx"
SERVER_ADDR	"200.23.222.19"
SERVER_PORT	"443"
REMOTE_ADDR	"216.73.216.147"
DOCUMENT_ROOT	"/usr/local/vufind/public"
REQUEST_SCHEME	"https"
CONTEXT_PREFIX	""
CONTEXT_DOCUMENT_ROOT	"/usr/local/vufind/public"
SERVER_ADMIN	"admin@localhost"
SCRIPT_FILENAME	"/usr/local/vufind/public/index.php"
REMOTE_PORT	"44019"
REDIRECT_URL	""" /Record/\n arxiv_https___arxiv_org_abs_2307_02638/Similar """
GATEWAY_INTERFACE	"CGI/1.1"
SERVER_PROTOCOL	"HTTP/1.1"
REQUEST_METHOD	"GET"
QUERY_STRING	""
REQUEST_URI	"/Record/%0Aarxiv_https___arxiv_org_abs_2307_02638/Similar"
SCRIPT_NAME	"/index.php"
PHP_SELF	"/index.php"
REQUEST_TIME_FLOAT	1790734978.7175
REQUEST_TIME	1790734978

Environment Variables empty

Registered Handlers

0. Whoops\Handler\PrettyPageHandler